Lets say in baseball somebody hits a ball hard enough to be a home run...?

If, while attempting a catch, you exit the field of play and complete the catch, it is an out. Even if you end up in the stands, as long as you still have the ball in your possession, it's an out. Same with foul balls too, by the way.

If the outfielder catches it while it is still in the air, it is an out. I have seen this happen a couple times.

My favorite example: A couple years ago, I was watching a Cubs/Brewers game. The bases were loaded and Prince Fielder came up to hit. He hit the ball and it would have been a homerun. However, Reed Johnson literally climbed the the wall and caught the ball even though it was past the yellow line. Fielder was called out but one guy did score on it as if it was the world's longest sac fly.

If the ball leaves the field, it's a home run. But if it's outside the fence and he catches it, it's an out.

No, once the ball leaves the park it is a homerun. Many of times has an outfielder jumped up to steal and homerun and on his way down his glove falls over the fence. This is considered a homerun. So if your whole body where to fly out of the field of play it is no longer an out. Foul balls are different because the players feet are on the ground when they make the catch. However if you jump and catch a ball it must return to the field of play to be considered an out.

Wooden bats have a different balance to them than metal bats so the problem might just be experience with the bat you're using. Other then that there are numerous other things that might be occuring. It is possible that you arent fully extending your hands, that youre rolling your wrists over, that the pitchers are pitching the ball in a place where your swing naturally hits from the top, or it could even be where you are hitting the ball off your bat. This is nothing to be upset about and if you are still hitting the ball hard it really isnt that big of a problem. Hit the cages and work on your swing.

As long as the player catching the ball keeps some body part in the rim of the fence, it is an out. if he is entirely in the stands at the time the catch is made it is not.

If he leaves the field of play and catches it its a HR.The rules say if a player leaves the field of play and catches the ball in HR territory it is a HR because the player is not allowed to leave the playing area.

If the player has to go OVER the fence and INTO the stands, it's a homerun even if he catches it there. He has to stay IN the park and catch it for it to me an out.

It's a caught ball and the batter is out. It doesn't matter if it's over the fence or not. You should youtube the Japanese outfield catch. This guy jumps up onto the fence and reaches out and catches a home run ball. Its crazy!