As far as I know we stick to the two electives we choose for the entire three years and that it plays a big role in Red's identity and how the story develops (especially in regards to which girls he can get to know). Though it would potentially be pretty cool to be able to end up taking all of them, I think it would be an additional can of worms, plus the other students presumably are to stick to the same courses.
Further I don't remember if it's been confirmed to have three semesters. In real life the University in my city has two semesters per year.
If I remember correctly after classes we have a set amount of free time where we can travel to different locations and see if events happen, I don't know exactly how much time each visit takes or if that's been decided yet.
A handful of characters do enter the Academy while Red is in second or third year, I think the wiki lists them but I don't know how up to date it is.
That was a lot of "I'm not sures" so hopefully someone else can confirm or deny.
Yes, this is basically correct.
We'd all love to be able to change electives and such every semester but from a writing standpoint that just isn't feasible. The VN is already overly ambitious with the amount of choices and variation in the dialogue that is possible, and that would kill us.