The President can only fire Comey for cause. Probably. It's not exactly clear if he can just fire them if he wants to now.  Usually if the President wants to replace the director they ask for them to resign.  He doesn't need anything for Congress. The Senate can impeach the director but would need cause as well.  

It's really not much of an issue. If the President asks you to resign, you resign.

It would take really big balls to not do so. It's impossible to do the job without the support of the President.

I actually don't think Trump wants him gone. If he does, it'll be next year before he acts. With all the shit going down it would look really bad, on top of that the Senate would need to confirm another FBI Director and the Senate has to confirm 100's of others as well right now.  He'll bite his tongue about Comey for now unless it's shown that he's fucked shit up. (Which is actually an open question at this point)