It's never been necessary to go to an elite school to be successful; it's simply much easier to get your foot in the door with employers if you have the words "MIT" or "Stanford" on your resume as opposed to "Coursera" or some random college. Moreover, employers COME TO YOU if you are at these institutions, you don't need to go out and beg for face time.
Depends on the major. I would say in many majors it's work experience that matters. I agree that the first job is easier to get when you're from Stanford, but that's it.
