Joh This is not correct. You have to pay some amount but it is no fee for the university.
There were some nominal tuition fees once (€500 per semester), but most states waved those, at least for EU citizens, years ago. There is often a mandatory fee for the student council work and such things, which may also include a public transport ticket. The fee may be reduced or waived in cases of financial hardship. Also, you still have to pay for food, accomodation, and similar non-academic fees, none of that is taken care of for you.
There are no special fees for long-term students in most states, but if you exceed the scheduled duration for your degree, there will be no more federal aid.