[RM2K3] PROBLEM WITH BATTLE SPRITES

That looks pretty neat! As for them facing backwards, it's because you're putting the enemies in the "wrong" place, by default enemies are always on the left. I think there are ways around this (im fairly sure somewhere, perhaps on Battle Layout, there's a Mirror Sprites checkbox) but if you can't find something like that to fix them, I'd say just make all the sprites mirrored themselves! XD
Tinker around with it. I think there are more capable people than me at answering this question though.

Well, the first thing that's clear to me is that the sprites are on opposite sides of where they're supposed to be. In VX Ace, you can get away with this if you're using Battle Symphony, because that lets you micromanage what all the actors are doing, but this is 2k3. Now, I don't know if the system actually does this when triggering a back attack (per Marrend's suggestion). I've never actually seen 2k3 do it like that, so I don't know. I do know that what you're showing in the database is not the correct way to place enemies. They're supposed to be on the opposite side, and I'm pretty sure you're placing your player character battlers on the wrong side, too. I'm guessing you probably want that particular aesthetic, but you can't have it in 2k3 without some kind of plugin involving actual coding. You could try flipping the actors over in the image files, but I don't think you'll be able to get them to work right on opposite sides of the screen, even if you can get them to look right.