I don't think Marvel had to kill Quicksliver, just elected to. There are rumors he could come back, but that is not a for sure thing. I personally like how he died and hope he doesn't make a return.
No, just to Fox and Marvel (Disney) They don't want to share otherwise they'd do what Sony and Marvel did and come to an agreement to share or something along those lines.
That was due to Marvel and Fox both having rights to those characters. Quicksliver and Scarlet Witch were X-men at one point, which give Fox the rights to the characters. They are also Avengers so that gives Marvel the rights to them. So they're separate.
Links that go in more depth...