1. Nope. If you kill the robot first, Lugae controls it and accidently pushes the self destruct button. If you kill Lugae first the robot will self destruct of its own accord.
2. If you're lucky he'll cast reverse gas again, cancelling the effect and allowing you to heal normally.
3. As long as he has the reverse status, chuck two Elixirs at him. If you don't want to waste them (or don't have any) use high powered healing spells on him. If he's not reversed use normal attacks and magic. He's weak against lightning so make full use of Rydia's Ramuh summon.