The investigation then reveals that they have a number of deleted questions with lots of downvotes.
Deletion or not, the post is going to have a very high negative impact on one's ability to continue asking questions. If you can't write good questions, it's best you sit in the sidelines for a while to watch (or read) the questions that are good questions and are possible examples for the Help Center articles for asking a proper question (and four bonus articles too).
A deleted question cannot be improved, so the users cannot get out of the question ban.
Yes it can! Taking myself as an example, I can edit my own recently deleted questions and if I think they are of high enough quality that matches the requirements of the site, I would take a risk and undelete it. In this case, I rather take on a few more downvotes than never learning what I did wrong. And how do I do that? I learn from the users who comment under my post, leaving suggestions on how to improve next time. There is a chance though for the post to basically revive itself, going all the way up even to a positive score!
A warning can be provided to low reputation users that would discourage them from deleting their own question and explain that even a deleted question will affect the ban. The warning should encourage the user to improve the question rather than delete it.
This is quite subjective. A question with a score like -10 should surely be deleted quickly. No user, new or old, should ever think that the question they posted was even salvageable. All you can do now is learn and to improve. But when does deletion more risky than a downvoted post? That's the true question here is up to the user who has a clear knowledge of one's question history.
A deleted question can only contribute to one ban. Once that ban period expires, the deleted question no longer counts.
True, this may help. But one must remember that they can be improved. Of course, if the question was voted to be deleted or was undeleted then deleted again, the question should have an very high negative impact or extend the ban. This may not be needed because a deleted question may be quickly overturned by better quality questions in the future. Bans aren't infinite and I really do hope that not all of the questions have been deleted...
Of course, once the ban has been casted, there's no real escape except for these cliche phrases:
Regardless of the user who is being banned, there really anything else you can do. It's put simply as learn and improve.