Typically the defendant is the City/ an agent of the City so the defendant (the City) pays.

Cities get a lot of money through taxes so one could say that it's paid for by taxpayers although it wouldn't be completely accurate as they have other revenue sources (fines, Federal money, etc).

Yes, generally the taxpayer pays. I work for a County local government. When we lose a case, we have our litigation insurance pay. Then the insurance policy rate immediately goes up.

Sometimes the government employee does something so agregious that we say "we cannot defend you: you are on your own" but that is really rare.