"Would auditioning for agents contravene her tourist visa?"

I am not a lawyer or in anyway a legal advisor. That said, it seems to me that auditioning is not working.

"Would busking, which she's also considering?"

My understanding is that where busking is permitted it is based on the right of expression so again I don't see where this would be working either.

I suggest seeking the advice of a solicitor to be sure.

Peace,
Ed