Is it considered a shot attempt if the player is fouled on the attempt?

most def.

Yes. If the clock is stopped and an inbounds pass is to be made, the clock will only restart when it touches a player. Therefore 3 seconds is plenty of time for a player to catch and shoot the ball,...

No it is not a shot attempt.

There is no official name for that shot. It is generally considered a layup, depending on how they shoot the ball.

yes