Affiliate Marketing Secrets

Is there a way I can put a trademarked logo of a popular company on something I intend to sell as kind of a parody? Can I just include a disclaimer stating that I’m not affiliated or associated with the company? If not, what can I do to make it legal if at all possible?

Hello all,
After months of trying to find a subleaser for my apartment, I finally found a prospective buyer for it. While filling out paperwork, the apartment management then told me that the new leasers will HAVE to be a university student, but state that they are not affiliated with the university. They also require the leasers to provide student ID, and their GPA.
They have no written permission from the University stating that this is okay, but could potentially cut into their income from their dorms.
I could see if they cater to university students, but wouldn’t they have to also take other leasers as well to avoid a lawsuit?
Are they legally allowed to do this, and should I inform the university about what they are doing?
So, can anyone shed some light on this for me?