Why do we only pray for things that are possible to happen?

There is nothing wrong with this question at all. It simply illustrates that God has established certain rules of normalcy of which he rarely violtates. When he does violate the paths of which he usually ordains the boundaries of life, it is an extraordinary miracle. Miracles like Moses parting the Red Sea, or Jesus raising the dead are not normal possabilities otherwise they would no longer be 'miraculous'. The reason why 'most' Christians do not pray for these things (some do and even convince themselves they are regularily answered although not provable to others) is that we innately know it is not God's will. God does not promise to answer any prayer that is not his will, so why waste the time praying for what we know he will not answer?

This is the confidence we have in approaching God: that if we ask anything according to his will, he hears us. 15 And if we know that he hears us—whatever we ask—we know that we have what we asked of him. (NIV, 1 John 5:14–15)

As far as genuine miracles go, it is understood in the Bible that an unusual divine knoweldge that it is his will through revelation and faith can make someone ask for what seems impossible and know with full assurance that it will be done. For example, David when he attacked Golliath knew it was God's will to cut the head off of that boaster. God gave David special knowledge and faith to do this. Such things are called 'gifts' as not everyone recieves them like everyday common graces to the faithful.

To one there is given through the Spirit a message of wisdom, to another a message of knowledgel by means of the same Spirit, to another faithm by the same Spirit, to another gifts of healingn by that one Spirit, to another miraculous powers, to another prophecy, to another distinguishing between spirits, to another speaking in different kinds of tongues,a r and to still another the interpretation of tongues. (1 Cor 12:8-11, NIV)

Now clearly these gifts, especially the extraordinary miraculous ones have not always been given by God. He decides when and to who they are given. They are gifts not rewards for good deeds. There are times in the Bible where they seem wholy absent and other times when they are very much in operation. In our days they do not seem that active, otherwise more people would be praying in the way you suggest and the media would be all over it having no means of explanation through scientific analysis.

In other words the question is not 'why do we not pray such and such' but 'why is it not God's will for such things to occur as frequently as it has in the past' or for those more charismatic folks, 'why do we not believe as much as those in the past'?

People of faith do go to God with all such requests, when they find themselves in those circumstances, yet their faith and trust in their God almighty do not waver, when at times these requests of healing of physical deformities are not answered. In spite of this they understand their God and know that He does exist. He is not supposed to be available for us like a Superman at our every request. He has His own plan for us and is uncomprehending to our finite mind.

Faithful understand that if God was to agree to our every request than each one of us would ask and pray that we may never die but continue to live for eternity. We can also ask Him to heal every disease and infirmity of all people in this world. But His plans are not our plans.

Isaiah 55:8 “Indeed, my plans are not like your plans, and my deeds are not like your deeds, 55:9 for just as the sky is higher than the earth, so my deeds are superior to your deeds and my plans superior to your plans.

What is best for us is not always physical wholeness. Paul the apostle prayed to have his "thorn in the flesh" removed, but God said, "No," because He wanted Paul to understand he didn’t need to be physically whole to experience the sustaining grace of God. (2 Corinthians 12:7-10).

From testimony of Joni Eareckson Tada on modern-day miracles, she says, "Man’s dealing with God in our day and culture is based on His Word rather than ‘signs and wonders’"

That answer, in short, would be something like this: "God can heal amputees/ physical deformities and will heal every one of them who trusts Christ as Savior. The healing will come, not as the result of our demanding it now, but in God’s own time, possibly in this life, but definitely in heaven. Until that time, we walk by faith, trusting the God who redeems us in Christ and promises the resurrection of the body."

Why such miracles were common earlier.

In the thousands of years of history covered by the Bible, we find just four short periods in which miracles were widely performed-the period of the Exodus, the time of the prophets Elijah and Elisha, the ministry of Jesus, and the time of the apostles. All the type of miracles that are mentioned in the question were performed during these periods.

While miracles occurred throughout the Bible (and they still happen), it was only during these four periods that miracles were "common." During these periods, God used miracles and direct communication with people in order to reveal to them His character and nature, as well as His plans and commands.

When Jesus came to earth, He also performed miracles to prove that He was indeed the Son of God and to foster belief in Him (Matthew 9:6;John 10:38). After His miraculous resurrection, He enabled His disciples to continue performing miracles in order to prove that they were truly His, so that people would believe on Him who sent them.

Therefore we can say that God has already spoken, and His words have been miraculously kept for us down through the ages. Now we need no further miracles to “validate” the Bible. In His perfect "Word" is everything we need “for doctrine, for reproof, for correction and instruction in righteousness” (2 Timothy 3:16). The Bible is complete and is perfectly able to make us “wise to salvation through faith in Christ Jesus” (2 Timothy 3:15). We need nothing more, and we are not to seek extra-biblical revelations. To do so calls into question the efficacy of Scripture which God has declared to be sufficient.

Prophet Habakkuk said: “The just shall live by his faith” (Habakkuk 2:4). God does not give His people a continual chain of miraculous signs; He expects them to trust what He has already done, search the Scriptures daily, respond to the Holy Spirit within, and live by faith, not by sight (Matthew 16:4;John 20:29).