At what point do the Basics move into their new rooms with their new roomates or do they keep the same roommates all the way through the first semester?
Usually they will be assigned new roommates from basic to first semester, then assigned new roommates for second semester. Sometimes a squadron will let the fourth-class cadets choose roommates, generally depending on their performance.
Near the end of basic last year, our cadet was allowed to list roommate possibilities (don't remember how many they got to list). He got 2 he listed (which were not his BCT roommates) and they stayed his roommates the whole freshman year.
They march back from the Valley on 24 Aug and have that final (winddown) week of Basic (25-31 Jul) and then they'll move to their Academic year squadron probably on 1 Aug, setup rooms, get class schedules, laptops, books, etc.. As was said, romates are completely dependent on each sqaudron.