Egypt will probably do nothing. However, that won’t stop Israel from hunting them down, even if it takes years. Unless the leaders remain permanently holed up, Israel will get them.
Mossad knows how to do wet work. It’ll be a black eye on El Sissy if it comes to that. But it’ll be trouble for him with Da Brudderhood if he does anything himself. So the least bad option for him is to quietly green-light Mossad, and then make some angry noises when they finish whacking them and saving any hostages still alive. Blahblahblah Egyptian sovereignty. Blahblahbllah, I wipe my a@@ on the Camp David Accord, etc., etc.
I don't think so. Egypt hates Hamas because they are as much a threat to them as the are Israel.