Now we're talking, precise questions!
You can catch the puck with your glove, but you can't keep it in the glove for more than like a half a sec or so. Can't score/pass with your glove, except passing is allowed in your own defensive zone (blue line marks this).
Fighting is "allowed"; 99% of the time it's two players who've planned this in the faceoff or even before the game. So it's entertainment, but sometimes helps a team gain momentum when the chips are down. So there's spontanious fights, too. If a star player of the team gets hit unfairly or something, the guy who did it might get "challenged". It's an unwritten rule that you "accept" the proposition to fight. The referees let the fight go on until a player is on the ice or hurt. Broken noses and such happen all the time, but the "pro goonies" are quite even in skills so it might end without any proper punches to the face.
As long as there's no intention to kick the puck in goal, it's allowed.