Would most of his original followers considered themselves Romans? What about most Jews? What about the other peoples of Roman Palestine?
Doubtful, only because the various peoples living in the Roman Empire were not consider Roman unless they were citizens, and outside of Italy only a small percentage of the population were. Citizenship was not broadly granted until Caracalla in the third century CE. The peoples across the Empire generally considered themselves part of their ethnic background, or place of origin (Gauls, Greeks, Egyptians, Syrians, etc.)