Throughout your time at the Academy, you have professional knowledge that you need to learn. This is one of the ways mids learn about the Navy/Marines and their equipment, personnel, and customs/history/traditions. 4/C do this on a weekly basis. They are assigned to learn a chapter in their professional knowledge books every week. Every Friday night (or alternate day for holidays, MOs, etc.), plebes will take a quiz to assess how well they learned the material. If they pass, great, if not, there is some type of remediation. The professional knowledge program is administered Brigade wide by the training staff chain of command.
Activity period is a very general time. I have never heard someone call it that, but I know what you are talking about. There is usually a block of time (1900-2000) that can be used for trainings, extra-curriculars, meetings, and mandatory events. The amount of midshipmen participating depends on what the event is. If it is an extra-curriculars, only club members are going. If it is mandatory, then the Brigade will go. Its use is all over the place. I had weeks where I had the evening to myself after dinner every night and weeks where I was busy every evening.
Study period (2000-2300 but 2200 is when you can go to technically) is a bit more regimented for Plebes than upperclass, but not by much in my opinion. Plebes can't listen to music, but they can choose where they study. Some go to the library, some a team space, and some stay on deck or go to a classmate's room. They just have to be back by 2200 unless approved to be out late. If they don't have homework for whatever reason, they can study professional knowledge or knock out other professional tasks.
For upperclass, study period more as the commonly accepted time to do homework and projects more than anything else. Most of your friends are probably doing homework, so it is easy to meet up and knock out projects or try and figure out how to get past step one on a thermodynamics problem (step one being writing the problem on the paper). For me, I did homework during sports period and I worked out during study period. Mac D (the NARP gym is a mad house during sports period). Even if you have homework, you're allowed to watch Netflix, hang out with friends, etc. As an upperclass, the expectation is you know what you need to do to manage your time. So you're allowed to manage it how you see fit.
