These are some interesting ideas. The thing is that having daily written homework assignments I don’t think is really necessary. For one, I personally think this could put a strain on the professors who would have to grade all of these assignments. They already work hard to create fun classes and have to grade quite a few assignments from those. You can still get extra experience from many ways, such as the daily riddle which you can do each day. You can also get help from others in completing the riddle if you are not very good at them. I know a few can be difficult but if you ask for help someone almost always knows the answer.
Perhaps instead Professors could make textbooks that students can optionally read for more studying?
As far as the broom steering, the reason you may be experiencing the sudden falls is because in the wilderness and diagonal lane for example there is a height limit in place to stop players from getting stuck or leaving the map. If you fly too high you will be brought back down closer to the ground.