I would suggest trying my other suggestion and trying to restore an old copy of your TWLN partition then. However, since you think it might be Luma, if you can find a certain iso site, the CFW Discussions section has something you might be interested in. Search for "AIO A9LH Configurations" and you will find some setups far more complete. Plaillect's guide is great for installing A9LH. My collection is for completing the experience by setting up everything he doesn't provide. I doubt the problem is Luma, but it can't hurt to try the other 6 CFWs and 4 other boot managers (I'd suggest starting with BootCTR9, it's my personal setup). If you can't find the iso site, there's an extremely stripped down version of the files
here, but try to find the proper release, because it includes every file you need already.
1. All the system needs in order to boot is "arm9loaderhax.bin" from your CFW or boot manager of choice (BootCTR9 needs its "arm9bootloader.bin" as well). So, technically, all you really need on a new card are "arm9loaderhax.bin" and your CFW's folder (in this case, that would be "luma" of course). You'll probably want the homebrew in your "3ds" folder, your HBL payload, your HB boot menu (boot.3dsx), etc. as well, though. So, it's perfectly understandable if you just want to back it all up and copy it to the new card. That's what most people do. Assuming you deleted EmuNAND like the guide suggests, there's nothing there to backup, so, just the card's contents. It's the "Nintendo 3DS" folder on the card you need to transfer over in order to keep your games and saves. Again, though, it depends on what you're trying to do. If you're setting up a second card to run more games and/or emulators, you would want to leave that folder out and let the system create a new one, for example. But if you're switching to a bigger card that's going to replace the previous one, you want to include it.
2. You don't. Yet, anyway. There are some on-NAND CFWs, but they hardly seem worth it to me. If the card reader breaks, I'll buy a new one and solder it on. In the unlikely event I destroy the system in the process, it was broken anyway, and now I've got an excuse to buy a shiny new "Hyrule Edition" model. An emergency NAND CFW would really only be useful if you have a Sky3DS+ anyway, since a broken card reader only leaves one place to load games from. I do own a Sky+, but I still wouldn't want to run a system that way. As soon as the card reader could get here, it would be coming apart.