I've known a few schools that were run by families. Of course the family members were ranked higher than the students; they'd have to be in order to teach.
As for the rest, I don't know why any of that would be a problem. Sounds like they want you to be fit (when is that BAD?) and to have a broad range of technical knowledge.
Again, every place is run differently. At my first karate school, our belt tests included a required, and progressively higher, number of pushups and situps, in addition to running. The last school I attended simply tested you on technical knowledge alone. I can't say which was better, but I definitely liked that one FORCED you to be in good condition. They also charged fees, though I can't remember exactly how much. So I don't know, nothing you said means anything out of the ordinary without having more context.
Could you link the website of the school? That would be helpful in judging if there is extra costs.
But with that said, yes, it could be a scam. Could you elaborate on the training of the instructors?
My martial arts school is a family run business. All the family members are high ranked. The rank tests all cost extra. I have to memorize many self defense techniques, some intercepting kick combos, many boxing combos, multiple katas, jiujitsu lock flows, a weapons form and be in fit physical condition.
