Refer to title.
I thnk it depends in part on the size of the incoming class. This year’s freshmen class was quite large. If there is some sort of medical reason you’d require a single, I recommend getting this documented and approved PRIOR to committing to attend K. That is the time you have the most “power” in negotiating this sort of thing.
Almost impossible. You need a well-documented medical reason and K implements a vetting process. There just aren’t that many. My D is a sophomore and the hall singles were gone early during the junior picks. There are singles available in suites to upperclassmen, but you need to have a group of 5-6-7 students wanting a suite that includes you in the single.