Currently, as far as I know, firmware 18.1.0 is fully supported by Atmosphere and Hekate, and sigpatches / sys-patch work. Other modules are probably being updated unless they already are up-to-date and working. Updating firmware on stock via official means should be fine and will work regarless if your console is banned or not.
If both your sysNAND and emuNAND are on the latest versions, you should be able to use your cartridges on both. On CFW, you'll need to enable game card reader for your cartridges to work. I haven't dumped any of the cartridges I own so far since it's easier for me to find the copies online and install them to the emuNAND. I do know that you can use nxdumptool for that, but if you just want to install your carts to directly to the console / SD card, you can do so via DBI, for example. Other installer will probably work, too.
Yep, that's how it is by default. You should have two Nintendo folders on your SD card, one on the root (that's the one used by stock / sysNAND), and the other one inside of emummc folder somewhere (that's the one used by emuNAND).