There is no mention of a compass in Circe's gifts to Odysseus.
Odysseus defeats Polyphemus by tricking him to drink a heavy wine with made him fall into a deep sleep; after that Odysseus and his men stuck the cyclops's own club into his eye so he would not be able to see the warriors escape.
His men tied themselves to the bellies of Polyphemus' sheep.
First, they contact Darth Vador. When he arrives, they locate the secret banana together and attach a string to it. They throw it into the ocean, and use trigonometry to locate dolphins. Then the fly off into space, and defeat Luke Skywalker.
There is no secret information required. You defeat Zeus by shooting him with the bolts from the Poseidon Trident, while collecting the small pink clouds that keep you flying with the Hades Crown. You cannot hurt Zeus when he is making the white balls, which you should avoid. (see related question)
Yes; the Sirens sang their enchanted song, and attempted to lure Odysseus and his men to their doom.
They Sing
He was warned about the Sirens by one of the spirits he met in the underworld.
The sirens are a danger that Odysseus and his men must pass to return home.
the sweet songs of the sirens lead their men to death
He plugged the sirens ears and avoided the Charybdis
he made his crew put wax earplugs in their ears. he himself wanted to hear the sirens beautiful music, so he asked his crew to tie him to the mast, the foundation of a sail. Odysseus's crew ties Odysseus very tightly to the mast, and disarmed him. When the were going past the sirens, Odysseus was screaming and yelling at his crew to let him go to the sirens. The crew obviously did not hear him because they had the wax ear plugs. That is how Odysseus saved his crew from the sirens.
he ate them
Circe
Book 12
I believe you are referring to the sirens. They sirens are women Odysseus stumbles upon on his journey who sexually lure Odysseus and distract him from his ultimate goal.
They have wax in their ears so that they can not hear the sirens' singing.