Q) If a ball lands out-of-bounds, but is returned by a player anyway, can it still be called OUT?
A) Yes. The simple act of returning an out-of-bounds ball does not keep it in play.
Q) If there is a disagreement on whether a ball lands IN or OUT, who has the authority to make the final call?
A) The players on the side of the net where the ball bounces (the "receiving team") have priority. If one of the receiving team players makes the call and the other player fails to see it, then the call made by the receiving team player stands. If the two receiving team players disagree on the call, then the ruling is made which favors the HITTING team.
Q) If a player from TEAM-A hits a high dink with a backspin, and the ball lands in TEAM-B's kitchen, then bounces back over the net and lands in TEAM-A's court without being touched by a TEAM-B player, is the ball still in play?
A) No. Prior to landing back in TEAM-A's court, the ball must be touched by a TEAM-B member for play to continue. A TEAM-B player is allowed to reach over the net, if necessary, to hit the ball, but the net must NEVER be touched by a player or his/her paddle. (Touching the net results in a fault.) If TEAM-A was serving, it's a point for them. If TEAM-B served, then loss-of-serve results.
Q) If a player from TEAM-A hits a ball that goes around the side of the net post (but not over the net) yet still lands in TEAM-B's court, is it a valid shot?
A) YES. This IS a valid shot and the ball is still in play. This link will take you to a YouTube video showing this shot in action. https://www.youtube.com/watch?v=NUjJh2PXPc8