Abraham tries to sacrifice his son. Is exploiting a human a moral behaviour?

While the sacrifice of another human is obviously not part of God's plan, this was a test of faith for Abraham. Hebrews clarifies this action

By faith Abraham, when he was tested, offered up Isaac, and he who had received the promises was in the act of offering up his only son, of whom it was said, "Through Isaac shall your offspring be named." He considered that God was able even to raise him from the dead, from which, figuratively speaking, he did receive him back. Hebrews 11:17-19

This wasn't simply the killing of a son, as horrendous as that would be. This is a test of Abraham's faith that God would fulfill his promises, and can be seen in contrast to Abram siring Ishmael (Genesis 16), where he took God's plan into his own hands.

Also note that the moral law was not revealed when this had taken place. The ten commandments would not be given for at least another five hundred years, and the covenants of grace certainly weren't established. Now when "God tells us" to do something, we have much more information to judge it against. God's relationship with Moses was really different, and largely based on trust rather than morals or law.

Let's lay some foundation from the start. (All scripture NIV)

God and Abraham had quite the relationship. God promised Abraham a son who would become a great nation (Genesis 17:15) even when he was 100 years old and his wife was 90. Abraham believed God and God provided him a son who was named Isaac (Genesis 21:2).

Isaac was the son God has promised Abraham, but as a test of Abraham's faith God asked Abraham to sacrifice his son Isaac on an altar as an offering to God (child sacrifice was a common ritual among pagans in that time period). From the very beginning of the passage the author of Genesis tells us that this is a test of Abraham's faith (Genesis 22:1). This was an unusual thing to do; however, it allowed God to show his faithfulness and also Abraham to show his faith in God. It's unclear to me from the passage whether Abraham believed that God would provide the sacrifice or if he knew that God could raise the dead (Gen 22:8, Hebrews 11:19).

The final verses in the passage say (Genesis 22:15-18):

¹⁵ The angel of the LORD called to Abraham from heaven a second time ¹⁶ and said, “I swear by myself, declares the LORD, that because you have done this and have not withheld your son, your only son, ¹⁷ I will surely bless you and make your descendants as numerous as the stars in the sky and as the sand on the seashore. Your descendants will take possession of the cities of their enemies, ¹⁸ and through your offspring all nations on earth will be blessed, because you have obeyed me.”

Faith is the key here, not blind obedience.

Much like Abraham was willing to give his own Son. God, the better Abraham, gave his own son to die for our sins. We see in the context of the New Testament that Abraham's sacrifice of his son was foreshadowing the sacrifice of Jesus Christ for our sins. The parallels are nicely illustrated in the following table:

Isaac (Genesis 22)                         Jesus

Only son of promise (v. 2)                 Only begotten of Father (John 3:16)

To be sacrificed in Moriah (v. 2)          Sacrificed in Jerusalem (2 Chron. 3:1)

Considered dead by father for              Dead for three days (1 Cor. 15:3-4)
three days (v. 4)

Carried wood for his own sacrifice (v. 6)  Bore his own cross (John 19:17-18)

Submitted willingly to father (vv. 6, 8)   Submitted willingly to Father
                                           (Matt. 26:39)

Raised from altar, his life spared by      Raised from the dead by
the power of God                           the power of God (Rom. 6:4)

Now, from the very beginning God's people has brought sacrifices as payment for their sins (Genesis 4:4 (Abel), 8:20 (Noah)). Later God mandated that Israel make sacrifices for atonement (Exodus 29:33,36).

Unfortunately these were imperfect offerings and were not sufficient to cover the sins of the people. They needed a better sacrifice (Hebrews 9:9-10). Christ was a perfect sacrifice for our sins.
Hebrews 9:11-14:

¹¹ But when Christ came as high priest of the good things that are now already here, he went through the greater and more perfect tabernacle that is not made with human hands, that is to say, is not a part of this creation. ¹² He did not enter by means of the blood of goats and calves; but he entered the Most Holy Place once for all by his own blood, thus obtaining eternal redemption. ¹³ The blood of goats and bulls and the ashes of a heifer sprinkled on those who are ceremonially unclean sanctify them so that they are outwardly clean. ¹⁴ How much more, then, will the blood of Christ, who through the eternal Spirit offered himself unblemished to God, cleanse our consciences from acts that lead to death, so that we may serve the living God!

This is not about modern day morals about God keeping his promises to Abraham and his people. God promised Abraham that "I will surely bless you and make your descendants as numerous as the stars in the sky" and "through your offspring all nations on earth will be blessed." The initial outpouring of this blessing was through the formation of the nation of Israel. However the perfection of this blessing was through the death of Christ and God granting us as Christians the status of Abraham's descendants.
Galatians 3:29:

²⁹ If you belong to Christ, then you are Abraham’s seed, and heirs according to the promise.

This is why Christ died, so that we might be children of God. He was a perfect sacrifice for our sins as foretold in the life of Abraham and Isaac. In the same way that God is a better Abraham, Jesus is a better Isaac. In the same way that Israel were Abraham's (and God's) children through the line of Isaac, we are God's (and Abraham's) children through Jesus.

Finally you address a moral concern about human sacrifice. This is an interesting question. For one thing I think it's to let us know that God takes this seriously.
Romans 8:31-34:

³¹ What, then, shall we say in response to these things? If God is for us, who can be against us? ³² He who did not spare his own Son, but gave him up for us all—how will he not also, along with him, graciously give us all things? ³³ Who will bring any charge against those whom God has chosen? It is God who justifies. ³⁴ Who then is the one who condemns? No one. Christ Jesus who died—more than that, who was raised to life—is at the right hand of God and is also interceding for us.

The second reason I have is this one, Isaiah 55:

 8 “For my thoughts are not your thoughts,  
     neither are your ways my ways,”  
        declares the LORD.  
 9 “As the heavens are higher than the earth,  
    so are my ways higher than your ways  
    and my thoughts than your thoughts.  
 10 As the rain and the snow  
    come down from heaven,  
  and do not return to it  
    without watering the earth  
  and making it bud and flourish,  
    so that it yields seed for the sower and bread for the eater,  
 11 so is my word that goes out from my mouth:  
    It will not return to me empty,  
 but will accomplish what I desire  
    and achieve the purpose for which I sent it.  
 12 You will go out in joy  
    and be led forth in peace;  
 the mountains and hills  
    will burst into song before you,  
 and all the trees of the field  
    will clap their hands.  
 13 Instead of the thornbush will grow the juniper,  
    and instead of briers the myrtle will grow.  
 This will be for the LORD’s renown,  
    for an everlasting sign,  
    that will endure forever.”   

Essentially, God is not bound by our human laws and morals; his ways are not our ways.