Schools are funded from the federal, state and local level, plus non-government sources (churches etc.). Police is state level, AFAIK. Fire department is paid for by an extra tax on fire insurance (so, I guess you could argue it's a property tax via extra steps), and state funds. For streets, it depends, cities pay for city streets. Autobahn is mostly federal, others are state, federal.
For the taxes, it's complicated, because there are some taxes for which the cities and states can decide the amount, and others (for example VAT), from which they get a certain fraction, but the amount is decided on the federal level.
Edit: Let me add: Property taxes are very strangely regressive. You pay it whether you rent or own, and there is a minimum apartment cost, so you'll always pay, while a low income might not be taxed at all. Then, often, there is a sudden jump from apartment complex to SFH.
