the Columbia housing office to see what listings they have, and to get answers to these types of questions? Usually good, expensive private universities like Columbia have helpful housing offices.
If I knew the answer to any of the questions, I would try to help. I am guessing it would be difficult for them to get accepted into a coop, but on the other hand, many rentals also have stringent regulations of annual income equal to 40x the rent or 80x for a guarantor.