It all starts when Peter Parker gets bitten by a radioactive spider. This gives him amazing powers like super strength, the ability to climb walls, and a 'spider sense'.
Spider - Man would probably be defensive at first. He's used to working alone most of the time, and being interrogated by the Avengers would seem unfair to him. He might crack some jokes to ease the tension, but also firmly state that he's a hero too.
The age of Spider-Man in those comics isn't fixed. It changes based on the plot. As for being dead, typically he isn't, but there might be alternate universes or special arcs where his fate differs.
Well, Andrew Garfield's Spider-Man gets his powers through a spider bite. This leads him on a path of self-discovery and a sense of responsibility, eventually making him embrace the role of Spider-Man to fight crime.