Mk so i don't have much of an answer and your questions confused me a little bit buuuttt here I go.
"Can I set up that L2+R2 hotbar to only appear for summoner/scholar and not appear(leaving a blank hotbar) when I am using my black mage?" - If you have it so that the hot bar is not shared (an option in settings) it should already be blank or only have the skills for thm/blm you have put on it.
Is it possible to make the L1 button, a "Change Hotbar Set(Backwards)" and make the R1 button, a "Change Hotbar Set(Forwards)"? - Not to my knowledge, but you can make a macro that changes it to the desired hotbar. I wouldn't be the person to ask how to write it specifically though.