With a single ticket you'll have to go to the check-in desk as I don't think the self-service machines are set up for UA-issued tickets. With an international itinerary, I would always prefer a human being over a machine for check-in anyway.

I don't think there are any rules regarding the age of guests, but this is irrelevant in any case: as others have said, you are allowed only one guest but you may get lucky with your second guest if you ask the reception staff nicely.