Would the phrase always imply "me", or could it also imply a him/her/them? I left off the "me" and Duolingo marked it wrong.
Just out of curiosity, is it more common to say "please" in the middle of the sentence than at the end, in Ukrainian?
This phraseology might be considered rude (or impolite!) in English, unless you know the person well. In common English usage, you might say something like 'Could/can you give/get/pass me a plate, please?' or 'Could/can/may I have a plate, please?' English people tend to be more formal, unless they know someone really well, i.e. with family and close friends.