Positioning one's self behind F2 and in the slot between F2 and the batter and switching side to side to accomodate LF & RH batters..... Is this a regulation mechanic??
Is there an advantage gained by making the switch? Could one always call balls/strikes from one side of F2 regardless of a RH/LH batter??? TIA

Yes, this is common and regular mechanic. It enables the umpire to see the entire strike zone, plus allows them to see any HBP, no matter how weak, and to see the bat as it enters the zone, not to mention the batter being hit immediately by their own batted ball. For this reason, I would recommend working the slot solely as opposed to trying to effectively umpire from one side of the catcher alone.

I umpired one game from the left side of the catcher. One. And I suspect I missed a HBP, based on reactions from the player involved. Work the slot.

(PS - the reason I worked the left side for 1 game ... league was shorthanded near the end of the season. I had stopped umpiring due to a broken rib. After being stupid, and agreeing to work bases for one game when they were desperate, PU didn't show. So I got on the gear and stayed VERY snugly behind the catcher. Probably the worst zone I ever had, as I was never comfortable back there.