TEE - Term End Exam (finals essentially)
Check out this link, West Point and the Army have a lot of confusing acronyms and this website helps with a lot of them.
http://www.usma.edu/dmi/siteassets/sitepages/newcomerinfo/what is that.xls
I am personally involved in the Paintball Club (tournament team), Ski Instructors Club, and Company Athletics Soccer. Paintball is for the times when it is not snowing and Ski Instructors is obviously when it is too cold/snowing and therefore I can't play paintball anymore. Company Athletics is basically intramurals, all cadets have to do some form of activity if they are not on a competitive DCA team or Corps Squad team (Corps squad teams are Division 1 teams).
For the weekends,
Fall: Lots of football games and therefore we have parade and then the game, otherwise there are A/C or A/D weekends that allow for military training (A/C) or study weekends (A/D). For the 3 day weekends, I try to get away and go enjoy New York or surrounding states. As a plebe you only have so many passes (weekends that you can leave post) and therefore it is good to sign up for free ones like the Tunnels to Towers 5k (which is a lot of fun and very symbolic). There are plenty of opportunities to do things, you just gotta look for them. Otherwise, weekends are very relaxed and are where you can catch up on sleep or your favorite netflix show (or Amazon Prime since students get it 6 months free).
Spring: There are no football games, therefore more weekends for training. I think my company has a shoot planned, Humvee licensing, rucking, and some other things scattered throughout the semester. There are still weekends available for pass but the best time for those is on 3 day weekends. Still, weekends are more relaxed and allow for a little R&R before you hit the heavy week.
Care Packages:
During Beast Barracks, or CBT, packages must be inspected by the Cadre since no one is allowed food or electronic devices. Socks and other types of things that people need are allowed but this is an inefficient way to receive them since it takes 6 days for a letter to get home, then another 3 or 4 for the package to get to the New Cadet with the stuff he/she needs. Bring things with you to R-day. During the academic year, you can receive almost anything. The mail room is always stocked with shipments from Amazon Prime or family sending love in the form of food. My mom sent me so much food that I was gaining weight pretty fast and I had to tell her to stop.
I hope this helped, let me know if there are any further questions!