Two questions about Matteo...(SPOILERS)

Hi. I had the same question, Matteo did not seem like someone who would commit suicide, because he was brave and didn't feel sorry for himself event though he did not have a good opinion about himself. But I think the whole thing was triggered by the encounter with Mirella. Matteo had felt like an outsider his whole life, he seemed very sensitive. You can see that when he decides to end his trip after loosing Giorgia, or when he drops out of Uni because of an argument with his teacher. It seems to me that he felt there was something wrong with him, with the way he saw things, and whenever he approached somebody, he hurted them. That's why he stays away from his family and from Mirella, and it is confirmed when Mirella comes to him so confused. Before he jumps out of the balcony he goes back inside and closes the glass doors, so I think he wasn't completely determined to kill himself, but then quickly opens the doors and jumps. So that's my opinion, he could live with his depression, but not with the idea of hurting others.
About why he said his name was Nicola, I think the point was that, he didn't want to relate to others as himself because he felt he hurted people, and also he wasn't able or willing to let somebody into his life. So he choses to present himself as somebody else and gives the name of Nicola, someone he obviously loved and admired and felt was much a better (and normal) person than himself.