https://3ds.hacks.guide/godmode9-usage#creating-a-nand-backup
Backup your NAND just in case. I also backup my SD card ~monthly in an encrypted archive file on my hard-drive and personal cloud. Better be safe than sorry, already happened to my Wii...
It isn't part of the original O3DS range in terms of specs, so yes. It will work on a New 2DS and New 2DS XL, as well as the expected New 3DS and New 3DS XL.
One thing is that Nintendo TVii was mostly a web-app, and here it will require you to build an actual app for it if you want something that complex as WiiMC. Could still be done even if i lose bit the practicality when you could just have an App...
Also, porting a close-dource game ain't something that can be done easily. At all. Atleast, you did request one that seems to be "realistically" runnable and potentially portable. But it still not that easy. Most of the time, the answer here, is...
You can already do that. I did try to my local media server interface. The issue, however, is the Wii U basic web browser. It doesn't support a lot of modern web features.