1) A player is in bounds when he is not touching the floor, an object other than a player or person or an outside boundary. The best easiest way to describe a player in bounds is "something touching in, nothing touching out". There is n requirement for both feet, hands, knees, cheeks, ears... etcA1 passes to A2. A2 catches the pass while airborne and throws it to the floor inbounds before landing out of bounds. A2 then comes back inbounds and is the first to touch the ball.
1) Is this an out of bounds violation? Does A2 need to establish two feet inbounds to be considered inbounds?
2) If not, did A2's throwing the ball to the floor count as beginning a dribble?
3) If it does count as beginning a dribble, if A2 touches the ball with two hands, dribble's over, right? Else if A2 bats the ball to the floor with one hand, he may continue dribbling, right?
3) Yes, one of the elements that defines the end of a dribble is when the dribbler (it already began) touches the ball simultaneously with both hands.
And Yes, he may in this situation bat the ball to the floor to continue the dribble he started by throwing the ball to the floor.