Well, if you're not going to leave him then what is it we can tell you? He's not going to change and you have discovered that this is the man you have fallen in love with. Do you seriously think you could spend the rest of your life being tricked, shit tested, spied upon and lied to? If the answer is "yes" then have fun. If the answer is "no" then you must break up with him, heal and then find someone sane.
This guy needs some professional councelling to get over his insecurity and lack of ability to trust. If he won't get that help, then it is very unlikely that he will ever change.
Maybe you shouldn't ignore it next time you see him staring in your classroom window and then running away so you won't see him (or he thinks you didn't see him). At least if you let him know that you don't like him doing it and that its disrespectful and it makes you unhappy then MAYBE he will try to control his inappropriate behaviour? If he doesn't think you think it's him or he thinks you don't know he stalks you at school and if he doesn't know that it really bothers you then he'll just keep doing it.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion