A comprehensive answer is out of scope and probably best given by a true accessibility specialist, but for example, if you only use <div> tags for everything, a lot of the screen reader's affordances for navigating are unusable. Images that carry information but not in their alt text are another simple example.
And then there are parts where JS could actively help. For example, if you have a tabbed interface, but clicking a tab results in a full page refresh, the screen reader loses all context.
Also keep in mind that there's more to assistive technology than just screen readers, e.g. sufficient colour contrast and keyboard navigability are important to many people. Too many websites still get those basics wrong.
Not necessarily, unfortunately. (Though I guess technically it's easier to throw up barriers using JS, but it's not an inherent quality, and leaving it out doesn't automatically make it good.)
Note there's a group of users that larger than the group of users without JS (for whatever reason): users of assistive technology. And they don't even have a choice.
While I'm all for considering the needs of every user... If you get to the point where you're worrying about no-JS users, I hope you've already considered the needs of people with disabilities, whether temporary or permanent.
Edit: oh right, wanted to add: just making a site work without JS doesn't automatically make it accessible to people with special needs.
I only really hear 3 (or at least, hear people imply it) in reality, and maybe a small nod to 7 recently. For 4, I see people think arbitrary numbers like 90% or 80% code coverage are things that matter.
"Native plants"
"Yeah!"