Yes, homework is common in many schools. Details can be found in the school Act of Hessen. But there are also schools that largely do without homework. Please inform yourself in the school program / at the school management about the regulations at the respective school.
You can find additional information at https://www.rv.hessenrecht.hessen.de/lexsoft/default/hessenrecht_rv.html#docid:7117322,38,20110916