I can answer a few of these, as I have had some experience with it already.
1- Judging by your response(and the prevous owner's) there is a high chance that it is running AutoRCM already (you can make sure about it by using Hekate's payload and checking under "tools - AutoRCM" more details here
https://nh-server.github.io/switch-guide/extras/autorcm/), so yeah, If the console runs out of battery or is turned off, you will have to send a Atmos' payload by either using TegraRCM on your PC or a dongle with the payload, I really recommend you getting a dongle as they are relatively cheap and will save you a ton of time and work. more info about how to do it here:
https://nh-server.github.io/switch-guide/user_guide/emummc/sending_payload/
2- You can either install the games using goldleaf or tinfoil, the file format that goldleaf supports is .nsp, and the installing process is rather simple, get the game on your SD if the file is below 4GBs(Fat32 won't allow you to place files heavier than 4GBs on your SD unless you partion it, but it is a tedious job), and install it directly from goldleaf, or use the remote install option with Goldtree if it is heavier than 4GBs. more info on that here
https://switch.homebrew.guide/usingcfw/installnsps/installnsps-goldtree
EDIT: about the compatibility isues, while installing some NSPs, goldleaf might tell you that you're missing sigpatches or that you firmware is too low, a partial fix has been posted by the user "Ryft", you can read more about that here:
https://gbatemp.net/threads/8-1-0-a...missing-sigpatches.547295/page-2#post-8780696
3- It might simply be the case of a faulty joycon, I have experienced it as well and only getting a new pair of joycons fixed it, though someone who knows another fix may be able to help you