It really depends on the chin too, how long cleaning will take. Chinchy's cage takes about 20 min. to clean, a couple times a week at most. I take his fleece liners outside, shake them out, clean up any rogue poops, and replace them. With every chin, I do a hay, food, and water check everyday, as well as giving them a bit of crushed rose hip or a couple oats occasionally and sticks daily. It can be tedious, but it's routine and not a chore for me.
As for your questions, most of them could be answered by looking over the first couple pages in the diet and nutrition and housing and supplies sections. For other queries, there's always the search option.
My concern is about your parents caring for your chinchilla once you go to college. Being on board is one thing, but I know I disagree with my parents on how to care for our cat that I rescued a few years back, and her needs are very simple. Are they going to provide the same quality of care that you would, including hay, food, water, cleaning frequency, and playtime? Finances are also another consideration. You said that you were going to pay for the cost of supplies, the chinchilla itself, etc., but are you going to do that while you're in college? And if you aren't footing the bill, it's presumptuous to think that they'll buy the same things, rather than taking cheap short cuts. Just something to think about.