Apparently the symbol of school in a dream can have various subconscious meanings (not metaphysical or anything), most importantly learning how to deal with our personalities. The symbol of a school or a school-type situation will appear when we are attempting to get rid of old ideas and concepts. It also denotes a difficulty of dealing with authority figures, and also has relevance with regards to learning about how to deal with relationships.

The significance of the male intruder most probably points to a need to defend yourself from something, but it could also possibly point to sex or a threat to your sexuality. I don't know if it is at all relevant, but the most obvious interpretation of the teacher would probably be a connotation of someone in your life trying to guide you in some way. Very obvious, and I don't know if it's relevant at all.

The terror that you felt in your dream probably refers to unresolved fears and doubts.
"It is only by experiencing such a profoundly disturbing emotion [in our dreams] that we are likely to make an attempt to confront those fears". The other girl's fear in the dream is a possible indicator of the fact that you are in a position to help someone else in your life with fears and doubts or something like that.

I don't know if any of what I just wrote is relevant or not, or if it makes any sense to you, but I find dream interpretation very interesting. I'm not saying that these are the true meanings of the symbols or what not, I'm just working from my dream dictionary. I find it quite useful and accurate most of the time. For instance, the other night I dreamt my right hand was rotting off and I had to cut it off with an axe. Apparently when you dream of the left side of your body it refers to your creativity. I used to love drawing and painting as I'm an illustrator, but recently I've been avoiding anything creative due to a lack of self-worth. So basically my dream was a subconscious reminder that I'm neglecting my creative ability and my love of drawing.

Hope my post was at least slightly entertaining if not helpful :-P