In doubles tournament play, if my opponent serves to me while his/her partner is off the court retrieving an errant ball, can he/her take the point if the serve is good and I choose not to return the serve?
I would generally say no. The serving team has to indicate to the receiving team that they are about to start the point, and the receiving team can legitimately say that they looked to the not-ready partner to see if the serving team was ready and got the indication of "no".
What if it's a legitimate ace?
If the receiver attempts to return the ball and fails, then they can't then claim they were not ready. Not sure what else you could mean by "legitimate ace".
Alternatively, if I return the serve and my return is good, can my opponent claim a hindrance and replay the point? What happens?
If they started the point, they don't get to claim they don't want to play the point. Then they've got to play it from whatever position they started it in.
I recently had this happen and my partner and I won the point. They claimed we showed poor sportsmanship and should replay the point. My response was that if a server puts the ball in play and I don't return it, I lose the point no matter where the server's partner chooses to be.
I think the two legitimate options here are either
1. Receiver attempts to return the ball and the point is played out to its conclusion, win or lose, regardless if this is in one shot (service winner) or multiple shots.
2. Receiver does not attempt to return the ball because they are not ready (because they are waiting for the serving team to be ready). That ball does not count for anything, server gets another serve instead.
Serving team does NOT get to serve the ball and then decide that they weren't ready to play after all.