Who is the bandaged man?

Ishmael is not an illusion, neither is the burning man that appears later on. One of the first cassette tapes given to you by Ocelot after the prologue is evidence that Ocelot also saw the burning man himself.

As for Ishmael, his identity is a major spoiler. He is heavily involved with Big Boss, so you should ask yourself twice if you want to read on.

He is Big Boss.

This inevitably leads to the next question:

Who is Venom Snake, if not Big Boss?

And the answer to that is (contains additional spoilers for GZ):

He is the unnamed medic who had to remove a bomb from Paz' stomach at the end of GZ. In TPP, he is unknowingly acting as a decoy for Big Boss.

All of this is revealed in mission 46: "Truth: The man who sold the world", which is almost an exact copy of the prologue mission 0, except for the beginning and the part where Ishmael leaves the ambulance, revealing his identity in the process. That mission is also the last story mission in the game, the missions following after that one being repeats of earlier missions.