This looks awesome! I'll have to practice my deutsch
I am understanding some of it though, that's good.
As for the range, an inscription claims that one of Genghis Khan's relatives shot a target at around 500 meters, though that was likely on foot. I'll have to look for that source though. I see no reason why 300 meters wouldn't be a reasonable maximum range for what horse archers could do, though sadly I don't think we have anyone today who can do that. Too few practitioners use Mongolian replicas of a high enough draw weight to achieve that range (I believe their draw weight was comparable to english warbows: they range from about 90-150 lbs.; this was their "heavy bow" though for long range or armor penetration; they likely had a lighter one for more rapid "kassai-style" shooting)
I think 300 meters was saying what those horse archers were capable of back then, not what the practitioners were doing now, which is probably more like 300 feet.
I believe at the Mongolian Nadaam (wrestling, horse racing, and archery) festival, there are three ranges: 75 meters, 90 meters (about 300 feet), and 120 meters I think, though I could have those ranges wrong, 90 might be the maximum range. That's for foot archery only though, and using a "padded tipped" arrow to knock one of those little rolled up things on the ground down.