The most important answer here is a question. Why did you create a new thread? This should be asked in the L4T thread (where all your questions are already answered). That, or the thread dedicated to setting up and installing software in Linux (also linked in the original post of the L4T thread).
That said, Linux on Switch has no access to internal storage. In other words, even if it somehow connected to Nintendo's servers (which, due to no storage access, it wouldn't know the servers to contact), Nintendo wouldn't be able to see your console's ID (again, due to no access). On top of that, since you're running Linux, it's going to look like a Linux PC, or tablet. This is just like if you installed Linux on a Windows PC. No one is going to know you run Windows, if you're connected while running Linux.
As for keyboard/mouse, check the L4T install thread (linked in OP of the L4T thread). First post gives pretty straight forward information. You can use bluetooth mouse/keyboard so no cables needed. Otherwise you must use the official dock (USB OTG isn't supported).