If you own (unlikely) or lease a hunting district, there are no further fees. You shoot it, it's yours.
If someone who is leasing/owns a hunting district allows you to hunt there, it's basically just another private contract with the terms you agreed on.
Hunting in Germany is based on a district system rather than a license system. If someone owns enough contiguous land (75 hectares in most federal lands), they can form a hunting district on their own, otherwise, the area of several landowners is pooled to form a hunting district and the landowners get to decide (by number of votes and the area behind those votes) what is done with this hunting district (e.g. they can lease it out, etc).
Quite a bit of hunting occurs from stands (which are quite luxurious compared to what I've seen in other countries), but stalking ("Pirschen") is allowed, too.
See above. If you're hunting in your owned/leased district, it's yours, if you have another arrangement, it's whatever the terms of this arrangement say.
No, not always. Usually, "group hunts" are more of an autumn/winter thing and as much social event as they are about hunting.