Germany varies massively by state, so you'd do well to consider Frankfurt and Munich to be in different countries when information gathering. Munich is incredibly expensive and it's very hard for foreigners to find a place to rent because demand far outstrips supply and foreigners are expected to be difficult to deal with and more importantly to move on - most landlords want to put a tenant in for life essentially for minimum hassle, and of course most houses and larger flats are rented out without a kitchen (no sink, no work surfaces, obviously no fitted appliances, just plumbing and wiring).
The Bavarian school system is unique and widely considered the "hardest" in Germany although many people of course dispute that. Children from other parts of Germany who joined my DC midway through Grundschule universally ended up at Mittelschule, and children who joined the Realschule from other states universally failed the years they joined but obviously this may be due to prejudice from teachers (my kids were born here and DH is German so they have a Bavarian accent so are protected from this) or just fluke due to small sample size - were rural so a less mobile population.
In Bavaria children start state school the September after their 6th birthday. They do 4 years of primary school. In march of the 4th year they get a report with grades which determine which of the 3 types of secondary school they can go to. Children with top grades don't have to go to grammar school but children with low grades aren't allowed to. 1 is the highest grade, 6 is a fail. A 2,3 average is required for gymnasium, 2,6 average for Realschule, anything below that and Mittelschule is the only option.
However there is considerable mobility later and Mittelschule entrants with good grades can choose to transfer after year 5 to Realschule and repeat the year there and carry on. The same for Realschule to gymnasium.
Rurally a lot of parents send children with 2,3 average to Realschule as boarder line or emotionally less mature children often really suffer and struggle at gymnasium (I tutored some of those kids who were permanently in tears and stressed to a cruel extent at age 10 and consequently chose to send my own 2,3 grade average children to Realschule).
School is only compulsory for 9 years - Mittelschule Abschluss ist at the end of year 9. This means some children leave school at 14 and 9 months. However they have to do an apprenticeship in that case.
Realschule Abschluss ist considered internationally as GCSE equivalent and taken at the end of year 10. UK boarding schools accept it as GCSE equivalent for admission to A level or international baccalaureate courses.
Gymnasium is 12 or 13 total years - the 12 year model was introduced recently but considered too intense so the move is back to 13 years. That's A level equivalent but a broader subject range.
Realschule children can transfer to gymnasium after year 10 if they have high grades, or go to Fachoberschule which is like a 6th form college.
Kindergarten here is absolutely excellent in my experience and all my kids were very happy indeed at kindergarten, but not everyone has the same opinion. It is cheap though not income related everywhere - that depends exactly where you live. The Vorschule Year for 5 year olds is free. Children are entitled to a place from the month of their 3rd birthday but there are more children than places and not everyone gets them.
Krippe (nursery) exists but rurally is not used much - unlike kindergarten they usually have spaces. However in Munich itself state nurseries are also full.