I’m accepted into the Environmental and Biological Sciences, and it says that Cook/Douglas is the residential area for that. Does that mean I am stuck there and can’t explore other campuses (College Ave, Livingston, etc.)? Do I even have to live in Cook if I am attending the Environmental and Biological Sciences?
No, on the housing application you can rank the campuses in order of where you want to live. Most first-years live on Livingston 
I think the housing application is closed even though I just committed to Rutgers (which seems early and dumb). Do I still get a preference? How does this work?
The housing application has been open for a few weeks and it’ll be open until early June. When you log into your enrollment pathway and make your Rutgers ID, you can access the housing application. Everyone ranks their campus preferences no matter how early or late they apply for housing, but it’s first come first served