A singaround will usually be organised by someone or someone will be nominated to direct proceedings. That person should be in charge of the rules and either make those rules clear and make sure they are followed.

As someone has already stated these events can vary in all sorts of ways, but the general rule is as stated, one singer for verses and all on chorus.

A separate issue is joining in with instrumental accompaniment. Again it needs to be clear what the rules are in that particular session.