I recommend that you watch the movie "W." by Oliver Stone. It'll clarify everything for you.
No. Movies aren't a good source of accurate information, particularly when they're produced by one person. What makes you think I'd trust it?
Why don't I direct you to something like, say, Fahrenheit 9/11 by Michael Moore? Because it's just propaganda.
A muslim once told me that it meant cutting off someones head because they don't believe in muhumad.
I've never once heard that as a definition of jihad.
Muslims can go into better detail, but my understanding is this: jihad is about internal spiritual battles. That is, it's about becoming a better Muslim. It has absolutely nothing to do with killing other people.