1A. It does mean “Pay for your [studies belonging to the college]”,”pay for your studies [(while standing) in/at the college]”, “pay for your [studies at the college]” since these three seem to have a pretty identical meaning to me. You could also translate to “Pay for your [college studies]”

1B. Not much to do here but looking at the context of the sentence and identifying the correct word groups i’m afraid

1C. Again the problem you have with the sentence is that you weren’t searching for the intended sentence structure, and for the other cases, here’s a valid example: “Payer le loyer au propriétaire” => “Pay the rent to your landlord”

1D. I don’t understand very well what you mean by that, but in most cases when there are two subjects in an english sentence it’s also the case in french (see your problem above for this particular case)

2. Because here it’s not the college as in national college of Paris for example, but college as an institution (like “you’re a college student”)