If I ask a question, then, for whatever reason, close it, what does it take, after that, for someone to comment on it? My understanding is that once a question is closed, all comments are locked so none can be edited or deleted and none can be added. Can someone with appropriate privileges re-open it, make comments, then close it again?
Closed questions are blocked from new answers, not from new comments. When your question is closed, it's still visible on the question lists, and nobody can answer it properly, but they can still provide feedback in comments. Closing a question usually takes five users with 3k+ rep, or one diamond moderator (with a couple of special cases around duplicate closure specifically).
Deleted questions are blocked from new answers and new comments, although they're still not blocked from being edited. When your question is deleted, it's no longer visible in any question lists or linked anywhere on the site, and it can't even be seen except by 10k+ rep users, and nobody except diamond moderators can post new comments on it. Deleting a question takes three or more users with 10k+ rep, or one diamond moderator, or you can do it yourself as long as the question doesn't have any upvoted/accepted answers.
If you close a question (which as the OP you can only do single-handed if it's a duplicate-closure reason), people can still comment on it, regardless of whether they have close/reopen privileges (they only need the comment privilege, which is obtained at 50 rep). Fortunately - otherwise how would we debate whether questions should be reopened or not, ask for clarification etc?
The only posts that can no longer be commented on are locked posts (which includes deleted posts), and locking a post can only be done by a moderator, or by triggering the spam/rude moderation bots.
Further reading (copy-pasting the whole thing does not seem relevant):