From what I understand a stalemated king passes nothing to the joker. Am I correct?
I'm sorry, I do not understand what you are asking. When a King is stalemated, the game is over.
I don't think this is the most natural interpretation of the Joker. I would opt for rules where the Joker keeps mimicking the previously moved piece after null move (just as it would after opponent Joker move).
There was a very long discussion about this on talkchess and another discussion here. The way I've programmed it was the concensus at the time, and for good reasons. I could change it, but I think you would like the results of that even less. It would forbid a lot of King moves. (The problem goes way beyond castling through check.) A King cannot move to any square that is attacked -- if the Joker still has its previous powers, it is potentially attacking a lot of squares and stopping the King from moving to them, despite the fact that if he did, the Joker would no longer be able to capture him because its powers have changed. Whether or not the Joker could actually capture the King on the next move is irrelevant. At the time of the King's move, the Joker either still has its powers or it doesn't. You can't have it both ways.
After some more consideration I would prefer the "null move doesn't change imitation" over "null move = King move" rule. Because then it would not matter whether you define check by a second move in the same turn, or as a move after a hypothetical null move. I am afraid the concept of a null move is only natural to engine programmers.
The Joker having the powers of the King when the other side is on the move is at least logically consistent. I don't like it, but then again, I don't like the Joker. Also, I don't understand why you are mentioning null move. I'm not sure what that has to do with anything.
I'm sorry, I do not understand what you are asking. When a King is stalemated, the game is over.
There was a very long discussion about this on talkchess and another discussion here. The way I've programmed it was the concensus at the time, and for good reasons. I could change it, but I think you would like the results of that even less. It would forbid a lot of King moves. (The problem goes way beyond castling through check.) A King cannot move to any square that is attacked -- if the Joker still has its previous powers, it is potentially attacking a lot of squares and stopping the King from moving to them, despite the fact that if he did, the Joker would no longer be able to capture him because its powers have changed. Whether or not the Joker could actually capture the King on the next move is irrelevant. At the time of the King's move, the Joker either still has its powers or it doesn't. You can't have it both ways.
The Joker having the powers of the King when the other side is on the move is at least logically consistent. I don't like it, but then again, I don't like the Joker. Also, I don't understand why you are mentioning null move. I'm not sure what that has to do with anything.