by Blair F..
I now suspect that the instructor didn't use the default reset settings and instead manually checked what to reset. He likely forgot to check the grades and that's probably why the student's assignments returned when he was re-enrolled. When I tested a reset in the backup of the course and re-enrolled that same student, I had no problems and there were no assignments attached to him.
However, problem #2 remains. The only way I could get around it, as an Administrator, was to find that student's assignments, unlock them all, then "login as..." that student and delete them. That's a heck of a lot of work.