Catches, runs, and boundaries are all possible if the ball touches the bat at any point, regardless of what else the ball may go on to touch. Furthermore, if the ball hits the pad before the bat, an LBW dismissal may also be possible.
Only if the ball does not touch the batsman's person may Byes be scored (Law 26.1), and only if it touches the batsman's person but not bat may Leg byes be scored (Law 26.2) (an oversimplification, but sufficient for the purposes of this answer).
Once the ball has touched any part of the batsman's person, he/she may not intentionally strike it again (other than to protect his/her wicket), as this would mean he/she was out hit the ball twice