Nuclear Engineering as a major was getting phased out during the 90s and early 00s. Eventually getting down to less than 20 schools. It's since stabilized and even had a brief uptick at the graduate level. But with the "nuclear renaissance" effectively dead, I would expect more programs to close up shop again. I doubt there will be many operating nuclear plants by the time I retire. I wouldn't recommend the major to anyone in high school now. The undergrad programs that survive will probably shift into something closer to Medical Physics or Radiological Engineering; traditional Nuclear Engineering might just become a graduate level major, similar to the few remaining Health Physics programs.
Yep, see below
Yes, there are a few niche programs out there, along with the super in-demand polymer and fiber engineering and paper engineering!
Yes, most of these program have just been consolidated into material science programs.
I doubt it'll ever go away entirely. Mining in general moves in cycles. We'll always need raw materials from the ground.
Maybe, maybe not? IIRC most lithium reserves are outside the US, and are often found in salt flats. Edit: I forgot about rare earth metals which is a totally different story, so yeah it could pick up again.