I suspect that student posting is technically not allowed, but your query has a lot of general interest merit to it and I will risk an exception and respond.
Trying to setup, install, and run postfix without any administrator privileges will be, um, interesting to say the least. Fortunately,Postfix is designed to run with the least amount of privilege necessary so this may be possible. You will need to adjust the main.cf file which controls which sections require root access and which run in a chroot jail. Aside from that, you will most likely need to edit the make and config files to set all the directories to a path off of your home folder. You may be able to do this by setting a build variable.
In any case you will really need to THOROUGHLY read the documentation, which is available on the postfix website. You may also want to get a copy of Postfix:the definitive guide.
Postfix is regarded as one example of a well written application. I suggest that you make the most of this exercise and try to learn as much about how and why it works the way it does.
