toomuchtooold sorry I've not been on for a bit.
There are Horts available for after school care, exactly what will differ wherever you are of course. As well as the Horts (which is after school care that starts immediately after school finishes), there were lots of after school activities. It will depend on your DC's ages as to whether they're big enough to take themselves off to something of course.
Neither of mine were at a KG (we arrived after DD2 was 6), but we lived round the corner from one - it was a Catholic one and they seemed flexible on when they arrived, judging by the people coming and going. Tell you what I thought was WONDERFUL, they also had a Wald KG which meant the kids spent all day outside in the woods, unless the weather was really really bad (it had to be baaaaad), when they had a little hut to retreat to. I used to run through the forest and hear them all playing, just such a good idea!
Children will arrive home on their own to look after themselves for a while a lot younger in the village I lived in, than I would have expected in the UK - that does affect what is provided and general expectations too I think. It did used to be (in W. Germany) that in nice middle class families mother would be at home to welcome the children back to a nice hot lunch, but of course that has changed a lot. DD1's class teacher was telling me she didn't think the system had quite changed enough yet to keep in step with that. But we did live in a village - I'm sure the offerings in a larger city would be much more comprehensive.
Oh and one more thing on your 7am question - a lot of people start work early and finish quite early too - so you could see people working in the offices in the town hall as the kids walked to school at 7.30am, and here too (Berlin) the morning rush hour is early, it's all quietened down by 8.30. So that will affect the KG hours too.