Category AM allows mopeds and scooters up to 50cc and a maximum of 45 km/h. In Baden-Württemberg you can ride a scooter from age 15. That's not the case in every German state.
Yes, AM covers small motorcycles/mopeds up to 50cc and a maximum of 45 km/h. If your scooter goes faster (including after tuning), that's illegal. Then you need A1.
As soon as you turn 16. There's no formal upgrade path. You take the full A1 training again (complete theory and practice). However, the AM theory from Baden-Württemberg is credited, so you save 2 double lessons.
Yes. AM allows any road except motorways and expressways. In practice, though, 45 km/h is limiting. On rural roads with 100 km/h traffic it gets uncomfortable. AM is ideal within town and on minor roads.