If you don't restore a clean NAND backup prior to going online, regardless if you're currently in CFW or OFW, you risk getting banned since traces of CFW persist even after the console is shut off.
Also, there is no "better" way to update as both have their pros and cons. Updating without burning fuses lets you retain the ability to downgrade in case future exploits come out for lower firmwares such as a hypothetical untethered coldboot but you risk getting banned this way. You can update officially which will most likely not lead to you getting banned (if done safely) but by doing so, you will irreversibly burn fuses rendering yourself unable to downgrade meaning you may be stuck using a jig and USB cable to boot CFW for a very long time. Weigh which one is more important to you, downgrading or being banned.
Kosmos has its own updater tool that you can use to update the package whenever there is a new version. You can use this without getting banned if you setup 90DNS on your Wi-Fi settings (they are literally just DNS settings). The offline alternative is downloading the latest Kosmos and replacing any files/folders from the old Kosmos.
If you want to transfer, make a copy of your Nintendo folder and rename it to Emutendo. By the way, the Nintendo/Emutendo folder only contains data for installed content on the SD card; it does not have any save data or content installed to internal memory.
Your SysNAND's firmware has not been patched for exFAT support. Either patch it by either updating to the latest firmware which will irreversibly burn fuses or with homebrew applications such as ChoiDujourNX. Or the simplest option is reformat the SD card to FAT32.
Retroarch had some Gamecube support however something happened which caused them to pick up support for the N64 over the Gamecube meaning the only option left is running Dolphin via Lakka which is not pretty. PS2 emulation will probably also be handled by Retroarch since there are no other PS2 emulators planned on being added to the Switch.
You can either use Hekate or SX OS to dump the NAND. I recommend using Hekate since, unlike SX OS, it can verify the backup. Hekate is a payload so you can either send it as the primary payload with a USB-C cable or chainload it from the SX OS menu.
While you can use ChoiDujourNX to update your SysNAND, if you want to play online without getting banned with SysNAND, it would be best to avoid using a homebrew application to update your SysNAND.
Right now, most people would say 6.2 is the "most desirable" firmware since it is the latest firmware and the exploit works on all firmware so most people are going to end up on the latest firmware one way or another.
When EmuNAND is first created, it is a 1:1 copy of your SysNAND so its firmware will be whatever your SysNAND was on when you created EmuNAND.
