Is there any clue/hint in the Bible that tells us “why or how” we won't sin on heaven?

The other posters have given very fine answers, I'm just going to cover this topic from one point that didn't make it in the other answers (That I could see). In Orthodoxy there is a concept called theologumenon which describes a "respected Theological opinion", which is something that many people believe, but not officially dogmatic.

In the vein of theologoumena, there is a viewpoint of the Afterlife called "the River of Fire", that has become quite influential, I include the a link so you can read an article on it. But in a nutshell, it describes the after life more as "states of being" rather than literal places you go to or are sent to. In other words, are experience of God in the afterlife depends on our spiritual condition. Christians that love God, will experience the fire of his love as euphoric joy, while people on other side will find it an unpleasant experience a little like an autistic person can find personal affection and closeness.

Anyway if the such a paradigm is true, I don't think that believers that are experiencing the raptures of Joy from being in perfect Communion with God would want to turn away from that. Because even Adam and Eve which had a close union with God in the Garden did not have that level of intimacy with Him that we will someday have.

Unfortunately, I can't provide a very detailed answer but I would say that one of the primary hints is in Philippians 3:20-21:

But our citizenship is in heaven, and from it we await a Savior, the Lord Jesus Christ, who will transform our lowly body to be like his glorious body, by the power that enables him even to subject all things to himself.

So not only will we have physical bodies in heaven, but they will be uncorrupted and incorruptible. I disagree that free will is the cornerstone of Christianity. Revelation 21:4 says that there will be no crying or mourning, which doesn't sound very free. Romans 8:7 says that the mind set on the flesh cannot submit to God's will, so it is 'unfree' in a different way. I would instead say that the cornerstone of the Bible is the sovereignt

Great metaphysical thinking here! I like your reasoning that leads to the conclusions:

• We can't blame the material world for the existence of sin.
• Experiencing the presence/power in heaven or via the Holy Spirit makes us unable to sin.

Before proceeding, I must point out a number of assumptions made in this question, not all of which are accepted by various schools of Christianity.

• Only the spirit/soul goes to heaven: a number of Christian denominations believe that while our present material bodies are left behind, we will be given a new physical body (Phi 3:20-21). There is also a system of belief that everything physical is stained by evil is known as Gnosticism, which was pronounced heresy back in the early centuries of Christianity.
• Free will is the cornerstone of Christianity: Actually, this is a hotly-debated issue by many Christian denominations. I highly recommend you do some research on this issue before claiming it is a "cornerstone."
• Adam and Eve sinned while in heaven: Yes, they sinned while in the Garden of Eden, but whether Eden = Heaven depends on your reading of Genesis. Gen. 2 places this garden "in the east" and at the head of a river that splits into the rivers Pishon, Gihon, Trigris, and Euphrates. If we take a literal interpretation of this passage, it seems to have been located in the middle east. If we take a mythological interpretation, then Eden = Paradise = Heaven.
• Evil can pop into existence: This is a statement of belief on the origin of evil, which is another hotly debated issue among Christians. You probably want to do some research on this before making a claim.
• Our "most pure stage" is a baby child: This relates to the issue of original sin and the sin nature, also hotly debated. You seem to indicate that babies don't have a sin nature, which is at issue with Psa 51:5.

Now to answer your question for Biblical clues that sin will be gone in heaven, I first suggest you watch this YouTube video. It explains a Biblical view of heaven, versus the common belief that it's a city where we sit on fluffy clouds and play harps. It also gives a clue of why there won't be sin in heaven: the sacrifice of the Lamb of God takes away sin.

Next, consider these verses for your question why:

• Rev. 21:4: There will be no more death in heaven (recall, death is the wage of sin per Rom 3:23).
• Is. 35:8-9, Rev. 21:8, 21:27, 22:15: Sin and sinners are excluded from Heaven.
• Phi. 1:6: God will complete his good work in us (i.e. sanctification) on that day (cf. 1Th 5:23, 1Jn 3:2)
• Hab 1:13: God does not tolerate sin in his presence, but paradise involves communion with God (Gen 3:8, Rev. 21:1-4).

For your question of how, that depends on your understanding of free will. You seem to believe in this doctrine, so I'll try to answer briefly within that system of belief (for an explanation of how from the contrarian belief system that there is no free-will, see this post by John Piper)

• Why do we sin? It is because of our sinful desires and enticement (Rom, 7:8, Jam 1:14), which is otherwise known as the sin nature.
• The absence of sin nature does not violate free will, since God has free will (Rom 9:11, 15) but no sin nature (Jam 1:13)
• Death destroys the sinful nature (Rom 6:7)

A fuller response from the free-will perspective is provided here.