Is it true that the Jewish view of Satan is different from Christians? Jews do not see Satan as a rebelling angel but an angel doing God's work.

Yup. Nothing in Judaism is apart from God, and the concept of an angel defying God is antithetical to Judaism.

In the beginning of Job, Satan shows up at a meeting of the “sons of God”, meaning the heavenly host, and no one questions his presence, other than asking why he came.

Satan is The Accuser or The Adversary. His job is to observe mankind and test human faith, in service to God. The only time we see him at length in the Tanakh is in Job, when God gives him permission to torment Job with increasing severity to test whether the man will lose his faith when things down not go well. Every single time Satan acts, he asks permission from God, and it is granted.

Contrary to popular belief, Satan does not appear in the Garden of Eden story. The antagonist there is a serpent, who at the time has arms and legs and can speak like a person. He tests the faith (or in this case obedience, since is hard not to believe in a deity when you live in his front yard) of the first couple. They fail, etc. At that point the serpent is made into a physical serpent.

There is no concept of a Devil in Judaism, nor in a Hell where people are tortured eternally, nor in a heavenly being who is able to defy God successfully and live as an eternal antagonist to him. You can thank Christianity for bringing all of that into the Abrahamic family, probably with inspiration from Zoroastrianism, for whom the eternal war between Dark and Light is a key feature.