Concerning Ultra Tag SSJ3 Goku & SSJ2 Vegeta, I've seen quite a few people say "Why does Vegeta lose his halo when he reverts to his Base form!?!". To answer that question, during their fight with Kid Buu, Vegeta requested Dende to make 2 wishes to Porunga: Restore Earth, and revive everyone who was killed since the World Martial Arts Tournament, but Dende changed the 2nd wish to reviving everyone who died since Babidi arrived, apart from the evil ones. That change included Vegeta, which allowed him to come back to life during the fight, right before he asked Goku charge the Super Spirit Bomb. So him not having a halo in Base form is correct.