Energy basically just functions as a "buffer" for Willpower, the stat that actually matters.
Willpower has a part in determining how successful the fuckboy will be in interrupting your character's actions (and how much of a problem hypno/drug actions will be). With a high Energy, the character's Willpower decreases less from getting fucked.
I'm not sure if the RNG is just kind to me or if I'm doing something right that other players aren't, but I've found it relatively easy to beat all three exams. Just focus on the subject each character's good at and use the booster items sold in the item shop (where you also buy clothing) before exams if you're having trouble.
My typical turn-order that worked for all 3 exams:
Turn 1: First and second girl select a Literature Q&A. Third girl gets a less-hard problem because she's relatively dumb. Fourth girl takes a Science Q&A.
Turns 2 through however-long-it-takes: Raise both the Logic and Knowledge bars through those actions.
Once both bars are full: Spam the "Answer" option.
Each successful Q&A answer is worth 300 points, so if 2 out of 4 characters succeed at answering the question it's enough. The girl who's relatively bad at both Science and Literature is a *godsend* if you end up losing and getting pillory'd - she does have the highest escape-stats in the game.
Also remember to use the recovery machine in the girls' dorm after every fight, because drug and hypno stats carry over and hypnosis snowballs *very* quickly - let it ramp up enough and you basically end up forfeiting every turn.
Using this method you can pretty much just power through the first exam without ever resisting, then repeatedly "tutor" the men's class to level up because it's basically one-on-one the first exam but with a much higher reward. At level 10 or so, you can power through the second exam in the exact same way - which then levels you up enough to power through the third exam.
Overall, it's an interesting concept for a game. However, the implementation is kind of a slog - the teachers' turns take way too long (seriously, every teacher gets to attack you 4 times per turn on average - that's 16 animations you pretty much just have to sit through before it rolls back to the attack-selection menu), the RNG can be *brutal*, and there's very little variation in scenes. I ended up deleting the game after a single run-through.