You create the academy at the storage.
1. Yes. Take 40 minus the level when the apprentice joined and that's how many honour points you get. However, if they join after lvl 30 you don't get any points when they graduate.
2. Then you don't get any points or graduates. It wouldn't make any sense for an apprentice to drop out at lvl 39 though, since he gets half of lvl 40's exp if he stays for one more level and graduates.
3. You just automatically get them, I guess...
4. At the storage you can spend them on Honour Sosun weapons. You need a lot of points though.
5. The accumulated exp buff that the apprentice gives you lasts for as long as there are points left on it, or max 24 hours. I don't know anything about the honour buffs you can get based on the number of graduates.