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.
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.
the timer has no idea if it was triggered during last boot. It only has the context of “this” boot, so it will do it right after a reboot and set a timer to start the service again after a week of uptime.
So if you reboot every day, it will trigger the service every day, even though you set it to weekly in the timer.
So it’s up to your .service file to determine if it has been run this week or not.