Does Judaism Believe in Satan?

Yes and no, as you've already discovered. In orthodox Judaism, there is a Satan figure, but he doesn't work against God. He is set up to be the tester of our hearts, or a tempter to draw us away from what God has called us to do.

There are many references to this throughout the Old Testament, but it wasn't until Jesus spoke of him as an enemy who was thrown from Heaven rather than a servant of God that sects of Judaism (Several of which were known as "Christians" several decades later) started to believe him to be an opposition force against God.

As was stated above, the first reference is in the garden, and God was not at all pleased with that serpent. IT has been said that the Old Testament is the New Testament concealed, and the New is the Old revealed.

Current Orthodoxy among Jews has been set up to protect Jews from believing the Messiah has come, much as was described in the New Testament. It is similar to Catholic orthodoxy, in that if a Rabbi who is esteemed has made a declaration or interpreted scripture in some way, we, today, are not permitted to question his observations because it is assumed, being closer to the last prophet Judaism recognizes, that they were closer to the truth.

Which means there can be no new revelation from God. Which, sadly, makes Orthodox Judaism very similar to Deists. So even if someone were to go through the Old Testament and realize this Tempter figure is, in fact, opposed to God, it would only because that person wasn't as aware of what God was communicating as those from many hundreds of years earlier when Christianity and Judaism split and Judaism did what it could to make itself a separate religion from those who were believing in the Messiah.