One thing I'd like to suggest is, if you're a singer and don't play an instrument, it's probably wise to state before starting whether or not you would like accompaniment.

Here in the UK, it's customary not to accompany or add to an accompaniment unless specifically invited. That does get relaxed a bit in a mixed tune/song session where most people have instruments with them. Even then if someone sings a capella, it's customary not to try accompanying.