This is pretty typical of a Chinese school. Often, even if you do have the proper documents to get a Z visa, they just don't want to pay the extra money, and a Z does indeed cost more.

As for the other details, this doe's not surprise me. Schools know that, for the most part, we don't want to teach primary school, while Middle school is not so bad. You have to be real careful, they are rather savvy at tricking you in what seem like the most innocuous ways.