Does anyone know the relationship between Zoroastrianism, Mithraism, and Manicheism?

Are they three separate religions or are they somehow related?

Yes........

They are all of the devil.........because they reject the Lord Jesus Christ

Zoroastrianism and Mithraism would be related in that they are both Persian religions. Unaware of the antagonist in Mithraism but in Zoroastrianism the god was a duel god. He was good and bad all at the same time. The last you ask about I am unaware of and will have to research it. Mithra is very similar to Jesus in his birth, death, and life. Mithra is an older religion that the Christians and it is interesting that they are so similar but really Christians take their stuff from Greek and roman theology so that they borrow things from Mithra is not very surprising.

They are three separate religions.

Manicheism is a religion based on the conflict between good and evil in the world and proposes a dualism that has light and darkness in conflict.

Mithraism is an ancient Persian religion based loosely on the signs of the zodiac. It has different forms, but roughly the story goes that Mithra "sprang from a rock", and killed a bull (Taurus, representing evil). Ancient Roman soldiers adopted Mithraism and brought it back to Rome. They would often have a ceremony where a bull would be killed as a replaying of Mithra's slaying of the bull.

Zoroasterianism is a monotheistic religion not unlike Judaism. It's founding and growth is strikingly similar to Islam, but was founded roughly one thousand years earlier. The "magi" of the nativity story in the New Testament are believed to have been Zoroasterian priests.

I don't know anything about Manicheism, but Zoroastrianism and Mithraism were both originally Persian religions. I believe that originally Mithra was an important god in Zoroastrianism.

This is NOT to be confused with the "Roman" god Mithra. They adopted him much later.

I did find an article that sums up information about Manicheism:
http://en.wikipedia.org/wiki/Manicheism
You can always verify the information through the sources used. It seems to me that the list is pretty extensive.

Perhaps the relationship is that they all originated in Persia, or in the surrounding areas.

But they are three separate religions.