During first stage both the SSME engines and SRB nozzles gimbaled to provide thrust vector control (TVC); the SRBs provided most of the control authority due to their long moment arm and high thrust.
For all of your sub-questions, the TVC would move the thrust vector slightly to rotate the vehicle in the desired direction.
Nose up pitch: nozzles deflect ...
There are 3 possibilities:
SpaceX deliberately rolled it
It rolled naturally, and SpaceX did not expect / want this
It rolled naturally, and SpaceX did expect / want this.
Looking at the video, the roll seems to intensify without any use of the rcs thrusters, so it seems likely the roll occured naturally. In this case, the torque that induced the roll ...