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.)