Does Christianity or the Bible forbid polygamy and widow remarriage?

Polygamy was practiced in the Old Testament but is not appropriate in the New Testament church. Elders and deacons should both be chosen from amongst those who have "only one wife" (1 Timothy 3:2 & 3:12). And if that us the ideal for them then it is the ideal for us all.

A widow or widower, however, may remarry. Marriages will not continue in heaven because there is no marriage in heaven. Our Lord specifically spoke on this (Matthew 22:23-30).

Does Christianity or the Bible forbid polygamy and widow remarriage?

Abraham had two wives:

Abram and Sarai tried to make sense of how he would become a progenitor of nations, because after 10 years of living in Canaan, no child had been born. Sarai then offered her Egyptian handmaiden, Hagar, to Abram with the intention that she would bear him a son.

After Hagar found she was pregnant, she began to despise her mistress, Sarai. Sarai responded by mistreating Hagar, and Hagar fled into the wilderness. An angel spoke with Hagar at the fountain on the way to Shur. He instructed her to return to the camp of Abram, and that her son would be "a wild ass of a man; his hand shall be against every man, and every man's hand against him; and he shall dwell in the face of all his brethren." She was told to call her son Ishmael. Hagar then called God who spoke to her "El-roi", ("Thou God seest me:" KJV). From that day onward, the well was called Beer-lahai-roi, ("The well of him that liveth and seeth me." KJV margin). She then did as she was instructed by returning to her mistress in order to have her child. Abram was 86 years of age when Ishmael was born.[Genesis 16:4–16] - [Abraham (Wikipedia)](Abram and Sarai tried to make sense of how he would become a progenitor of nations, because after 10 years of living in Canaan, no child had been born. Sarai then offered her Egyptian handmaiden, Hagar, to Abram with the intention that she would bear him a son.

After Hagar found she was pregnant, she began to despise her mistress, Sarai. Sarai responded by mistreating Hagar, and Hagar fled into the wilderness. An angel spoke with Hagar at the fountain on the way to Shur. He instructed her to return to the camp of Abram, and that her son would be "a wild ass of a man; his hand shall be against every man, and every man's hand against him; and he shall dwell in the face of all his brethren." She was told to call her son Ishmael. Hagar then called God who spoke to her "El-roi", ("Thou God seest me:" KJV). From that day onward, the well was called Beer-lahai-roi, ("The well of him that liveth and seeth me." KJV margin). She then did as she was instructed by returning to her mistress in order to have her child. Abram was 86 years of age when Ishmael was born.[Genesis 16:4–16]- Abram and Sarai tried to make sense of how he would become a progenitor of nations, because after 10 years of living in Canaan, no child had been born. Sarai then offered her Egyptian handmaiden, Hagar, to Abram with the intention that she would bear him a son.

After Hagar found she was pregnant, she began to despise her mistress, Sarai. Sarai responded by mistreating Hagar, and Hagar fled into the wilderness. An angel spoke with Hagar at the fountain on the way to Shur. He instructed her to return to the camp of Abram, and that her son would be "a wild ass of a man; his hand shall be against every man, and every man's hand against him; and he shall dwell in the face of all his brethren." She was told to call her son Ishmael. Hagar then called God who spoke to her "El-roi", ("Thou God seest me:" KJV). From that day onward, the well was called Beer-lahai-roi, ("The well of him that liveth and seeth me." KJV margin). She then did as she was instructed by returning to her mistress in order to have her child. Abram was 86 years of age when Ishmael was born.[Genesis 16:4–16] -Abraham (Wikipedia)

The Patriarch Jacob had four wives:

Jacob's marriages

Arriving in Haran, Jacob saw a well where shepherds were gathering their flocks to water them and met Laban's younger daughter, Rachel, Jacob's first cousin; she was working as a shepherdess. Jacob was 77 years old, Rachel was 14, and he loved her immediately. After spending a month with his relatives he asked for her hand in marriage in return for working seven years for Laban the Aramean. Laban agreed to the arrangement. These seven years seemed to Jacob "but a few days, for the love he had for her." When they were complete and he was 84 years old he asked for his wife, but Laban deceived him by switching Rachel for her older sister, Leah, as the veiled bride. In the morning, when the truth became known, Laban justified his action, saying that in his country it was unheard of to give a younger daughter before the older. However, he agreed to give Rachel in marriage as well if Jacob would work another seven years. After the week of wedding celebrations with Leah, Jacob married Rachel, and he continued to work for Laban for another seven years.

Jacob, having been celibate until the age of 84, fathered twelve children in the next seven years. He loved Rachel more than Leah, and Leah felt hated. God opened Leah's womb and she gave birth to four sons rapidly: Reuben, Simeon, Levi, and Judah. Rachel, however, remained barren. Following the example of Sarah, who gave her handmaid to Abraham after years of infertility, Rachel gave Jacob her handmaid, Bilhah, in marriage so that Rachel could raise children through her. Bilhah gave birth to Dan and Naphtali. Seeing that she had left off childbearing temporarily, Leah then gave her handmaid Zilpah to Jacob in marriage so that Leah could raise more children through her. Zilpah gave birth to Gad and Asher. Afterwards, Leah became fertile again and gave birth to Issachar, Zebulun, and Dinah, Jacob's first and only daughter. God remembered Rachel, who gave birth to Joseph and Benjamin.

After Joseph was born, Jacob decided to return home to his parents. Laban the Aramean was reluctant to release him, as God had blessed his flock on account of Jacob. Laban asked what he could pay Jacob. Jacob suggested that all the spotted, speckled, and brown goats and sheep of Laban's flock, at any given moment, would be his wages. Jacob placed rods of poplar, hazel, and chestnut, all of which he peeled "white streaks upon them," within the flocks' watering holes or troughs in a performance of sympathetic magic, associating the stripes of the rods with the growth of stripes on the livestock. Despite this practicing of magic, later on Jacob says to his wives that it was God who made the livestock give birth to the convenient offspring, in order to turn the tide against the deceptive Laban. As time passed, Laban's sons noticed that Jacob was taking the better part of their flocks, and so Laban's friendly attitude towards Jacob began to change. The angel of the Lord, in a dream back during the breeding season, told Jacob "Now lift your eyes and see [that] all the he goats mounting the animals are ringed, speckled, and striped, for I have seen all that Laban is doing to you", that he is the God whom Jacob met at Bethel, and that Jacob should leave and go back to the land where he was born, which he and his wives and children did without informing Laban. Before they left, Rachel stole the teraphim, considered to be household idols, from Laban's house.

Laban pursued Jacob for seven days. The night before he caught up to him, God appeared to Laban in a dream and warned him not to say anything good or bad to Jacob. When the two met, Laban said to Jacob, “What have you done, that you have tricked me and driven away my daughters like captives of the sword?" He also asked for his stolen teraphim back. Knowing nothing about Rachel's theft, Jacob told Laban that whoever stole them should die and stood aside to let him search. When Laban reached Rachel's tent, she hid the teraphim by sitting on them and stating she could not get up because she was menstruating. Jacob and Laban then parted from each other with a pact to preserve the peace between them. Laban returned to his home and Jacob continued on his way. - Jacob (Wikipedia)

In the Old Testament, widows often married their next of kin.

Tamar and Judah

After Shelah had grown up, Judah became a widower. After Judah mourned the death of his wife, he planned on going to Timnath to shear his sheep. Upon hearing this news, Tamar disguised herself as a prostitute and immediately went to Timnath which was en route to Judah's destination. Upon arriving at a place near Timnath, where two roads met, Judah saw the woman but did not recognize her as Tamar because of the veil she wore over her face. Thinking she was a prostitute, he requested her services. Tamar's plan was to become pregnant by this ruse so that she might bear a child in Judah's line, since Judah had not given her to his son Shelah. So she played the part of a prostitute and struck a bargain with Judah for a goat, secured by his staff, seal, and cord. When Judah was able to have a goat sent to Timnath, in order to collect his staff and seal, the woman was nowhere to be found and no one knew of any prostitute in Timnath. (Genesis 38:12–23)

Three months later, Tamar was accused of prostitution on account of her pregnancy. Upon hearing this news, Judah ordered that she be burned to death. Tamar sent the staff, seal, and cord to Judah with a message declaring that the owner of these items was the man who had made her pregnant. Upon recognizing these items as his security, Judah released Tamar from her sentence. Tamar, having thus secured her place in the family as well as Judah's posterity, gave birth to twins, Perez and Zerah. Their birth is reminiscent of the birth of Rebekah's twin sons. The midwife marks Zerah's hand with a scarlet cord when he emerges first from the womb, though Perez is born first. Perez is identified in the Book of Ruth as the ancestor of King David. (Ruth 4:18–22) The Genesis narrative also makes a note that Judah did not have further sexual relations with Tamar. (Genesis 38:24–30)

According to Ethiopic tradition, Perez became the king of Persia. - Tamar and Judah

However most Christians believe men should only have one wife.

Cleave to wife

Most Christian theologians argue that in Matthew 19:3–9 and referring to Genesis 2:24 Jesus explicitly states a man should have only one wife:

Have ye not read, that he which made them at the beginning made them male and female, And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh?

Husband of one wife

Many critics of polygamy also point to the Pauline epistles that state that church officials should be respectable, above reproach, and the husband of a single wife. Hermeneutically, the Greek phrase mias gunaikos andra is an unusual Greek construction, capable of being translated in multiple ways, including (but not limited to): 1) "one wife man," (prohibiting plural marriage) or 2) "a wife man" (requiring elders to be married) or 3) "first wife man" (prohibiting divorcés from ordination).

In the time around Jesus' birth, polygamy (also called bigamy or digamy in texts) was understood as having several spouses consecutively, as evidenced for example by Tertullian's work De Exhortatione Castitatis. The Apostle Paul allowed widows to remarry (1 Cor. vii. 39. and 1 Tim 5:11–16). Paul says that only one man women older than 60 years can make the list of Christian widows, but that younger widows should remarry to hinder sin. Some conclude that by requiring leaders of the Church be one woman men, Paul excluded remarried widowers from having influence. This would have been a more strict understanding of monogamy than Roman law codified, and would have been a new and unusual demand on men. - Polygamy in Christianity (Wikipedia)

Most denominations, if not all, allow widows to remarry.

The Bible forbids neither polygamy, nor widow remarriage.

Remarriage:

For the married woman is bound by law to her husband while he is living; but if her husband dies, she is released from the law concerning the husband. So then, if while her husband is living she is joined to another man, she shall be called an adulteress; but if her husband dies, she is free from the law, so that she is not an adulteress though she is joined to another man. - Romans 7:2,3

Polygamy is often practiced in the Bible, but never forbidden or condemned. The list of polygamists who are recorded to have multiple wives at the same time includes Moses, Abraham and David, who the Bible displays as central and exemplary figures of godly living. There are even laws surrounding the treatment of multiple wives, e.g. Exodus 21:10

If he marries another woman, he must not deprive the first one of her food, clothing and marital rights.

Nevertheless, polygamy is can still be a sin, and is a sin in today's society, for other reasons. As Richard puts it

Polygamy is a sin because it goes against the law [of secular society]. The law is in place because it is a carryover from the paganistic societies of ancient Rome. Preventing polygamy was not a biblical concept, but one that came after Jesus, after authorship of the bible, and after the genesis of Christianity. [...] We Christians are told to uphold the law and subject ourselves to the [secular] law

In the linked answer you find a more extensive treatment of polygamy in the Bible.

Christianity forbids polygamy but allows widow remarriage.

I agree with you that Gal 3:28 is not usually cited as support for the rejection of polygamy, because the passage context is about unity of Gentiles and Jews in Christ (notice the contrasts of social groups in the verse). Ken Graham already covered the OT view of polygamy, so I will not repeat it here. Ken also covered how the criteria of elder's marriage shed light on monogamy, so I will not repeat it here either.

The NT support for rejection of polygamy is based on what Jesus said in Matt 19:3-9 as the original intent of marriage before the Fall. I think in general Christianity agrees that marriage is to be a symbol of God's covenant between Jesus the bridegroom and The Church the bride, prefigured in the covenant between God and Israel. Read the whole book of Hosea which revealed the exclusive love that God demanded from Israel as a proper response to God's exclusive love for Israel, His chosen people. Hosea is a very touching book of how God STILL wanted Israel to come back to Him, even after Israel did "polygamy" and "adultery" by simultaneously worshiping other gods. The theme of monogamous relationship continued on to the NT period where there is only one Church and one Jesus. So it makes sense that the covenantal relation between husband and wife should be modeled after the relation between Jesus and The Church (see Eph 5:21-33)

This booklet on The Bible's Teaching on Marriage and Family (pdf here) is an excellent, easy-to-read, theological exposition on why Christianity espouses monogamy as well as the purpose of Christian marriage and how Satan wants to destroy it. The booklet contrasts between the secular notion of marriage as contract versus Christian notion of marriage as covenant.

On the other hand, NT teaching on widow remarriage is more on a prudential basis, far less dogmatic than the teaching on monogamy. The main relevant passages are embedded on Paul's recommendation to the churches he founded in Corinth (1 Cor 7 esp. vv 39-40) and Ephesus (1 Tim 5:11-16) so that the members of the church can grow toward holiness (you can get this sense from the circumstances which precipitated the 2 letters). Thus, Paul's advice on widow remarriage is to prevent distractions, temptations, and sins from polluting the local church body (example: like bad yeast in 1 Cor 5). Notice the overall context of the passages: the importance for a man and a woman to channel their desires into wholesome patterns instead of into deviant ways that the enemy (Satan) can use. This is because one theme of the overall teaching of Paul is the importance of holiness so Christians can enter the Kingdom of God (i.e. receive their promised inheritance) on the Day of Judgment (see 1 Cor 6:9-11, Gal 5:19-21, Eph 5:1-5).

See also a gotquestions.org article on What does the Bible say about remarriage after the death of your spouse? commenting on the same NT passages plus some OT background, saying that widow remarriage is "absolutely allowed by God".

The care of older widows (1 Tim 5:16) who cannot provide for themselves was a carryover from the OT ethic for helping the weak, which became the basis of why God condemn the powerful Jerusalem elite who instead of using their power to protect the weak they use it to oppress "the widows and the orphans". So Paul's teaching about widow remarriage should also be read in the immediate context of how the local church should choose which widows to support.

In modern North America (USA, Canada) and Western Europe, the situation has much changed since the NT period since:

1. women now have equal rights and opportunities to pursue their career
2. there is not much social stigma to single career women
3. there is nursing facility and social security payments for older widows
4. household arrangement is more nuclear than extended, so less "temptation" from busy-body younger widows living in the same household

Therefore, the churches have a lot less responsibility to care for widows than in Paul's period so this impacts the prudential judgment about whether widows should or should not remarry. But there is still a lot that we can do today. This scholarly article titled The Order of Widows: What the Early Church Can Teach Us about Older Women and Health Care describes the practice of the early church in light of Paul's teaching in 1 Timothy as well as the OT practices mentioned above as a background to what we can do today to help modern elderly women.

The NT is rather silent on the reunion of the marriage bond in heaven. Two frequently cited NT passages on marriage in heaven are Luke 20:34-36 and Mark 12:18-27 with sample interpretations in Why is there no marriage in heaven? and Marriage in Heaven? Will We Know and Love Our Spouses in Heaven? respectively.