I should probably know this - but why is it montre-moi and not me montre? I guess I'm confused about moi and toi vs me and te??
I think it always changes in imperative, both the position of the indirect object and the form. If you want to state the fact, "You show me the menu," you say "Tu me montres le menu." But if you want to command someone, "Show me the menu," you say "Montre-moi le menu." It's the same for other pronouns too, "Tu te laves" becomes "Laves-toi," "Tu lui donnes le livre" becomes "Donne-lui le livre," etc.
No, it's a question so montre-moi is the inverted and correct form. (Please correct me if I'm wrong, I'm not a native French speaker by any means!) That would mean something like "please, I show you the menu" which doesn't make much sense.