No... Jane and her brother Alec are just part of Volturi's guard. Aro's wife is Sulpicia, Caius' wife is Athenodora, and formerly Marcus' wife was Didyme,who was Aro's sister but he killed her.
Aro killed his sister, cause he didnt feel a use for her anymore. Marcus doesnt even know till now. Well Aro was just after might from the beginning on, so if he doesnt need someone that will happen.
He also killed Didyme because Marcus was thinking about leaving with her. He didn't want Marcus to leave so he killed Didyme. It basically sucked out the happiness from Marcus and that's why he is expressionless and un-emotional.
No, because they are already married. Aro is married to Sulpicia. Caius is married to Athenodora. Marcus is married to Didyme. So Jane is not a girlfriend of one of the three brothers.