The mayor can hire and fire whenever he wants, over the positions he controls. Our system of government is based on checks and balances. You are correct, the mayor was elected. And so was the council. Interesting that 5 councilmen (and women) can agree on things, and the mayor and the council can't - who's the problem?
As far as the attorneys, we the taxpayers get screwed. But once the mayor took the step of hiring an attorney, he left the council no choice. They have to be represented. If you feel the mayor's lawsuit was a matter of principal, why couldn't the council defending itself be a matter of principal.
I feel I have spent way too much time on this because I really think both sides need to get together, but this notion that the mayor is all powerful is wrong and against our system of government. You need the branches of government to check each other to ensure the other doesn't run amok.