I have both of the above problems.  Three of my rigs have been rented for 30 hours, stuck at the "Awaiting one confirmation".  And my payment sent to my wallet this morning is also stuck, zero confirmations, but seen by 7 peers.  Blockchain.info says "no such transaction".

There's something wrong with Betarig's wallet right now, and I don't recommend using this service until they fix it.