Yeah, the "can you assign the issue to me" is the most common. I don't even understand where it came from - does anyone ever actually formally assign issues to anyone?

But they absolutely also create PRs even if you say "don't create a PR. You don't know what you're talking about"

I'm pretty sure there's some guru/teacher that gives assignments to their students. The assignment is most likely "find a repo and ask if you can work on it." The student then either finds something easier to work on or gets points just for trying.