1. I don't think they do befriend the students, however they do become acquaintances which can help with charisma journal challenges.
2. You don't get a school bus (imagine carrying that around in your pocket
). At one of the higher levels you get the option to "Give Great Lecture" to give the Sim receiving the lecture a 20+ moodlet.
As I remember, you can also give lectures at the school.
3. I'm not really sure what you mean by this. Any YA Sim or older fills the other posts of teacher.