The ghost of the mage is the spirit of Gauldur, and after he appears, he is supposed to reforge the amulet for you. He is not hostile... he's one of the good guys. You can't talk to him -- he is supposed to appear, smack his son's spirits with a blast of magic, cast a spell to reforge the amulet for you, and then vanish back into the Aetherium from whence he came. You can loot his skeleton, though... he has a bunch of gold in his coffin...

-Loth
PS It sounds like your end-sequence got messed up by a glitch. Try doing the encounter with the brothers again?