If you are talking about gifts, and not food, then you can get them the same things you would get anybody else. As long as the product does not contain animal products, you're fine.
It can be on either or both. I would suggest gathering on Christmas eve with distant relatives just in case of a storm or something you can reschedule to Christmas, or you can have one day for...
Could refer to spherical ornaments on trees ( rarely used by themselves- though I have seen holiday wreaths with balls attached, rather like a ferris wheel, or Balls in the sense of festive dances...