I wonder whether the visibility of a post changes according to the user's reputation asking the question. Is it also known if a user's posts' visibility is affected by other actions, like having mistakenly flagged a question, an answer, or a comment as inappropriate?
It depends on where you're looking, but in general, the visibility is only determined by the timestamp (either of the last activity, or of the moment the question was created). However, on the homepage, questions with a score of -4 and lower are hidden. In any case, reputation doesn't matter; Stack Exchange is all about the content, not the person who wrote it.
Your flags don't have anything to do with whether your questions are visible or not. (With a reputation of 11, you can't even flag anything except your own posts, FWIW.)
2$\begingroup$ Perhaps "the Stack Exchange software is all about the content, not the person who wrote it"—the community, in which I include myself, definitely does not react to content in a manner that is blind to its author. (And I think that if it were all about the content in the deepest possible way, then author names wouldn't even be shown.) For example, I trust this Meta answer more when I see it's from you; from someone else I might wonder if they fully understood the system. $\endgroup$– LSpiceDec 17, 2020 at 22:25