1) Car tax calculator, as Mariusz mentioned, depends on engine type (diesel car is times more expensive than petrol car), age of the car etc:
http://www.bundesfinanzministerium.de/Web/DE/Service/Apps_Rechner/KfzRechner/KfzRechner.html
2) Insurance calculator, it depends heavily on drivers past (age, when got licence, previously insured cars in Germany etc). It's pretty expensive first years but then gets cheaper over time:
https://www.check24.de/kfz-versicherung/
3) Technical inspection, for newer cars every 3 years, older every second year.
4) There's no road tax currently in Germany for personal cars.
To my knowledge there's nothing else mandatory.