If I create a thread, can I post something like "all posts after this post must follow this new local rule" and will that be enforced by mods as local rules in the Op are?
If you mean, if you post in the OP "All posts must be in this format" or "No posts about this topic will be allowed in this thread" Then yes, that is a local rule to the thread, and people violating that rule will have their posts removed if reported. If you mean to make it complicated and say "all posts after post #3 must be *insert rule*" that is probably a little unnecessary.
That said, keep your request reasonable. If its something like, no posts with the word "the" are allowed in this thread, the local moderator might ignore it. If you want to set a rule that might be hard for a moderator to moderate, or you want to have the posts deleted promptly, I'd recommend making the thread self moderated. But something like the examples I gave above are fine.