Jesus again wanted to teach the Pharisees that they must not use God's law forbidding work on Saturdays as a reason to refuse to help people. Herodians were backers of King Herod, the man whom the Romans had appointed to be ruler of the Jews. Idumea was the province south of Judea. Tyre and Sidon were citieson the seacoast, north of Israel. Read 9 to 11.
Unclean spirit means the same as evil spirit or demon.
They are not people who have died. Rather they are evil angels who assist Satan in fighting God. Jesus did not want the demons to say who He was. That would not bring honor to him. Jesus would have His own ways to tell people who He was.