Wont go inte networking, but assuming networking works between them you can manually specify an IP in the mobile app:

Add a device -> three dots in top right -> add devices by IP.

Bonus: This also works over tailscale and similar apps, making it so you can have an always on connection despite not being home.

If your data is very important you should definitely prioritize implementing your backup for at least the most important stuff. You could probably move it over, but in case something happens your data will most likely be gone, or best case very hard to recover.

Fedora is a great distro, but they are decidedly bleeding edge on purpose and IMO not the best choice for a server hosting critical data.

A better option would be running a hypervisor like proxmox (you can even convert your existing Debian install, but I havent tried this personally) and passing your GPU to a virtual machine that runs fedora.

This gives you both a very stable environment for your data and and a bleeding edge environment where your hardware decoding likely works great. I do this exact thing personally and it works great.

Yes, its possible to check. Data has to be sent through some connection, and we are able to monitor all traffic going through connections we control. Its not happening on wifi and not on 4G/etc. So unless there is some other connection that is not a real issue.