And what if you DO mean to say "Give the menu, please" ? Maybe you're asking someone to give the menu to someone else, not yourself. For example, could you say "Дайте йому меню" ?
I think that the word "мені" is implied in this sentence, and that you'd have to put the pronoun in any other case. I can't be absolutely sure of this, though.
In English you cannot say "Give the menu". It should be "give me" or "give us".
there's no "meni" in the ukrainian, so i didn't put a "me" in my answer. why was i wrong? is the "me" implied, and if so under what circumstances?
It's a typical Ukrainian phrase to ask for a menu in a restaurant or a cafe. "Me" (мені) is implied. If you meant "him," "her," ..., you would specify that.
This is similar to Czech: “Dam si menu”, but the correct translation to English for Czech is “I’ll HAVE the menu”. We would never say “Give me the menu” in English as it is rude. Would this same “I’ll have” apply in Ukrainian, or is there a more polite way to ask for something?
Yes in English the typical way would be to say "Could you please give me the menu?" if we want to practice the verb "give" here. We typically ask "Можна меню, будь ласка?", which is "Could [I have the] menu, please?". This is how I would ask it at a restaurant.