First, when it asks me to put in my college, do I put in the college I'm *currently* in or the one where I'm going to actually be getting my degree from?
To the best of my knowledge you should put the college you are currently attending at the time of the application.
Second, in the Yearly Income, do I put my income (which is something but not very much) or my parents' income (since I am a dependent)?
This is tricky question and unfortunately I do not know the answer. Some credit card issuers have almost circumvented the credit card reform student card requirements by allowing the inclusion of grants, scholarships, and parental contributions in figuring the income amount. I do not agree with that practice
and imagine it will change but as of Feb. 2011 many issuers are doing it. Whether Discover does or not I do not know but I talk more about their cards here in my sponsored writeup about them:Discover Student credit card review
If it were me applying, I would use my regular income amount (excluding the above items) even if it is low. Card issuers do not expect students to be making much and many reportedly have annual income requirements as low as $2,000 from what I have heard in the media.