Basically, fighting games are beat 'em ups, technically, but with levels and enemies and stuff.
How to make stuff get hurt is explained in the novice tutorial you must have read of. Or do you mean you want them to play an animation when they get hurt?
Swinging stuff up is used through y vectors, in the set x/y vector action, which belongs to the platform behavior.
And, you know? For starters, you should make your character not punch, but create a projectile that shoots, or an explosion, like in my Action Gamemaster game when you press Z. That is, for starters. Trying to do punches and stuff is complex, and you should learn more about C2 engine before that. For now, try to develop the rest of the game while punches and kicks and stuff are substituted with something simpler. Or, you might try to create a different kind of game just for training.