Is there any Scriptural support for claims about Jesus appearing to Muslims in dreams and visions? I've heard many testimonies and claims about Muslims converting to Christianity because Jesus allegedly appeared to them in dreams and visions. For the interested reader, these are some example sources making such claims: 1, 2, 3, 4, 5, 6.
Is there any biblical support for this phenomenon? Can we find any parallels or prophecies about this phenomenon in Scripture?
Nowhere in the Bible will you read of any prophecy about Jesus appearing to Muslims in dreams and visions.  Perhaps that’s because Islam (and Muslims) did not exist till the 7th century.  https://en.wikipedia.org/wiki/Islam#History
The first-hand evidence you provided of Jesus appearing to Muslims in dreams and visions is overwhelming and undeniable.  There can be no dispute that such miraculous events happen today.  It is also worth mentioning that such dreams and visions are not exclusive to Muslims.  But if you want parallels or prophecies of this from the Bible, then you must realise that the words Muslim, Mohammed or Islam are not to be found in either the Old or the New Testaments.
Acts 2:17 quotes a prophesy from Joel 2:28, which says this:

In the last days, God says, I will pour out my Spirit on all people.  Your sons and daughters will prophesy, your young men will see visions, your old men will dream dreams.

The prophecy in Joel does not say that people would have visions of Jesus, because Jesus had not yet appeared in the flesh.   In the past people had visions of God and since the incarnation people are now having visions of Jesus.  The key point of this particular prophecy which pertains to the last days is “ALL people”, which embraces Muslims.
The Old Testament records visions and dreams given to a variety of people.   The Lord spoke directly to Job out of a storm in order to chasten him (Job 40:6).  Eliphaz the Temanite (one of Job’s comforters) had a most fearful dream in the night, and a word was brought to him:

A spirit glided past my face, and the hair on my body stood on end.  It stopped, but I could not tell what it was. A form stood before my eyes, and I heard a hushed voice: Can a mortal be more righteous than God? Can a man be more pure than his Maker?  (Job 4:12-17)

Dreams and visions were given to Joseph and Pharaoh (Genesis 37 and 41) and to Nebuchadnezzar (Daniel chapters 2 and 4).  They all came from God, usually as warnings.  These days, God communicates to us through his Son (Hebrews 1:1-2), sometimes through dreams and visions.