A: No. Keepers which give you some benefit for discarding or giving them away are supposed to be a cost to gain the benefit. If you are forced to move or discard, it won’t count as your sacrifice. For example, if you discard one of your Keepers because of a Keeper Limit, you don’t get to gain the benefit of the sacrifice. That’s an independent penalty.
However, if it’s your turn, and you are going to have to discard Keepers at the end of your turn anyhow, it would certainly behoove you to decide to use that power during your turn, so that it’s not wasted by the Limit.
If it’s not your turn, however, you can’t take that benefit if you discard because of a Limit. These benefits for moving/discarding a Keeper are like other Free Actions and, while they are “free” they can only be used on your turn.