My comments about independence were triggered by:

Recall that the way we rationalized away money risk aversion was to claim that money units become less useful as our wealth increases. Is there some rationalization which shows that utility units become less pleasing as happiness increases.

The independence axiom says "no" - I think - though it is "just" an axiom.

For the last question, if you drop axioms you are still usually left with expected utility maximisation - though it depends on exactly how much you drop at once. Maybe it will just be utility maximisation that is left - for example.