Do I have to deregister in Germany, and is that enough for tax purposes?

Under registration law yes: section 17(1) of the Federal Registration Act requires anyone who moves out of a dwelling without taking a new one in Germany to deregister within two weeks of moving out. For tax purposes, deregistration decides nothing. Whether a residence continues follows from section 8 of the Fiscal Code and therefore from the actual circumstances: anyone who can still dispose of a dwelling has a residence there, deregistered or not. Both need doing, but only one of them ends unlimited tax liability. General information, not tax advice.