I should describe aspects that I like about the University as a whole, and the major, right?
^Yes. Perhaps, even a discussion on the department can do favors for you?
And there are several places where I cannot avoid using "Computer Science".
^Well, there is always a way to get around it.
The same goes for "Carnegie Mellon University", with CMU. Is it all right to abbreviate these two things?
^I do not know about the CS in brackets, but I think that CMU should be fine. Not too sure however, but I definitely would assume that it is alright.