According to the leader of the SNP in Westminster the parents are the Duke and duchess of wessex not Sussex. It's Earl of wessex and he's Harry's uncle.
No Prince title by right, it needs royal assent or the queen to bestow it on him. It'll happen by rights when prince Charles becomes king. If he doesn't (abdication in favour of William) then I'm not sure he'll ever become a prince.
You've baffled me now ?