Life is made from the remains of stars, in order to prevent new life from evolving the universe would have to be destroyed. So the universe would still exist and new forms of life would take our place
Yes all material items would still be there but it'd pretty much just be a bunch of floating rocks; in my opinion, if theres no life its pretty much gone.
Yeah. Just because we're not here to observe it doesn't mean it magically stops existing. Matter operates differently when it's not being observed, but it still exists.