Hi! I encountered all of these problems in high school, so here are some of the things that worked for me:
1) Mouldy reeds -- Either put holes in your reed case (whether through drilling or some other method) or leave your reed case open for at least an hour after you play. Or when you get home from school. You can soak the already-mouldy reeds in hydrogen peroxide or antiseptic mouthwash, but honestly if they're mouldy they're more or less ruined and that's not a good long-term solution.
2) Biting the reed -- I struggled with this all the way into freshman year at music school, and the solution for me was to use more air to support the notes. What ended up happening was a teacher had me lay on the floor with a book on my stomach and fill my stomach up with air so that the book moved up when I breathed in, and moved down when I breathed out. Then he had me sit up and play, but he put his hands firmly on my shoulders so that I had to use my stomach instead of moving my shoulders. If you don't have someone to hold your shoulders down, you can also practice in front of a mirror.
If your problem isn't too little air (although those are good exercises regardless), try using lighter reeds and consciously tell yourself to stay open. But honestly, I thought my biting was due to a lot of factors and it turned out to be simply the air, so I would strongly suggest to try that first.
3) Tight high notes -- Again, put a lot of air into them. :) Also -- and I realize this is discouraging -- but the bassoon you're using might also be keeping you from playing nice-sounding high notes. I learned the Rite of Spring excerpt while playing on a Fox Model 4 (the plastic one), and it was a battle to the death because the instrument had a terrible high range. But now it's one of my best excerpts, so I guess it gets better?
4) High notes cracking -- Make sure you're using the right fingerings, and check the half holes on the high A-flat and D so that it's not too big or too small. (The former tends to be too big, the latter too small, in my experience.) You can check around the IDRS website or try Google for alternate fingerings.
Hope that helped a little? If you have any other questions, you can feel free to contact me! ♥