I've honestly no idea how the education system works for foreigners. If you're a foreigner living in the country, it's free, but I don't know what the conditions are if you want to send your child to school in Germany if you don't live here. - You don't have to pay, that's for sure, but I'm likewise sure that there are plenty of other conditions and regulations.

The school year starts in August or September. It varies from year to year and from Federal State to Federal State.