The Sixth Sense (1999)

Answer: Cole knew that Malcolm was dead as early as the first few scenes. When he opens his door to the house he doesn't immediately step out. Almost as if he didn't want to go out that day. After he finally muster up the courage, he waits for Malcolm to look away as he hurriedly makes his exit. He also picks up his pace as Malcolm begins to follow him. He knew from the very first time he saw him, and yes he was just as afraid of Malcolm as he was of the other ghost.

Answer: Yes, of course. Remember that Cole tells us that these ghosts only "see what they want to see". To avoid giving away the whole plot twist of the movie, we see Malcolm as he sees himself - no injury, and dressed as would be appropriate for where he sees himself. But we know Cole can see dead people, and he sees them as they truly are. The young blonde boy with the back of his head blown out should make this clear. As for the second part of your question, I think Cole is scared of Malcolm at first. You can see his fear when Malcolm walks past him in the church to sit in the pew in front of where he is playing. His tension slowly eases during their conversation, but he still looks wary as he leaves the church. I get the impression that Cole spends large portions of his time in this building, yet he leaves this time within a few minutes of arriving; he doesn't want to stay near this new ghost. He becomes comfortable with him later of course, and Malcolm eventually wins his trust through honesty about his own problems, but this is not true from the start.

Answer: I think we have to assume, while it is never said, that Cole is not afraid of all ghosts, just some that are angry, upset or creepy. He has talked to them, as evidenced that he knows Latin phrases, or the guy killed in Vietnam in the specific division and province. So while a bit scared of all of them, he is willing to talk or listen a little, but not enough to know they want his help. Then, here comes a child psychologist who knows how to talk to kids and get them to open up a bit, and Cole starts to trust him. But he certainly seems to know he is a ghost. While it is not said, he probably knows the difference between seeing a ghost and a live person always.