Not all lay-ups hit the backboard for example a finger roll.
Yes, that's how, sometimes, the ball gets stuck on the hoop. It gets wedged between the backboard and the side of the rim.
Only if your the person who did not shoot the ball
If the ball bounces off the backboard or rim and you catch it before it hits the ground it counts as a rebound.
only if the ball comes off of the rim or backboard of the basket
A 'bank shot' is a shot that hits the backboard before going through the ring for a score or not going in to create a rebound situation.
If a player shoots and it doesn't hit the backboard or rim, and they catch it before it hits the floor, it's a travel. The ball either has to: a) Hit the rim or backboard. b) Hit the ground before the player can retain possession again.
If it's an airball then no. If it just hits backboard then you aren't supposed to be able to but I see certain players do it all the time.
Yes, as long as the ball hits some part of the goal, its not traveling.