As far as I know, SP is an electron application and if you run Plasma in a wayland session, global keyboard shortcuts won’t work, unless you enable it in the Plasma settings.
I’ve had no issues saving to same folder as source when doing batch transcoding queues on Arch Linux. As long as the input and output files does not have the same filename it’s fine.
The couple of apps I use through flatpak has not had any issues as far as I can tell. Other than maybe being a little slow to get pushed to the newest version.
In a normal domain/DNS scenario, you need to make sure your domain points to the correct IP. Most registrars have websites where you can manage which domain points to which domain in the DNS records.