3. Later in 36 or in 37 CE Vitellius visited Jerusalem and re-organised religious affairs there.
He dismissed the high priest Caiaphas, known from the gospels, and appointed Jonathan, son of Ananus. Vitellius agreed that the vestment of the high priest should be kept in the temple in the custody of the priests.
From the time of Herod I. until then it had been stored in the stronghold of Antonia in the custody of the Herodians.
4. At the beginning of the Armenia crisis Herod Antipas was reserved. He was powerless against the Jesus revolt, but kept on the Roman side and closed the cities against the rebels. In a long-lasting revolt this could lead to conflicts, but not in a short one.
In the case of John the Baptist Herod Antipas decided to take action and have him beheaded before John could play a part in the revolt.