I can`t add to what the other members have suggested already regarding diet and the best way forward. All I will say is this isn`t a good scenario for your hamster as he will find it difficult to cope if he has broken or missing teeth and will possibly get by for a time and then could lose condition or suffer, so given the vet suggested putting to sleep, I know that`s not always worth doing, but the injuries sound quite bad without further vet intervention like making sure the teeth are okay, trimmed or that he isn`t unnecessarily suffering in silence.
Was he chewing on cage bars before this happened? You said that his nose was `split`? Poor soul, that must be sore.
Did he fall or get his face trapped?
Really hope he starts to pick up again but these injuries, especially to the teeth can be an ongoing concern. x