Connect the internet connection directly to the router, then connect the router to the wall ports. If it doesn't have enough ports, connect the router to a TP-Link switch, and then the switch to the wall ports.
Wall port 3 only connects to one device (PC) so no further action needed.
Wall port 1 connects to 2 or more devices, so connect the wall port to a TP-Link switch and then from there to your Nintendo Switch docks and the Pi
After that unless you've done some weird configuration your gear will all be on the same subnet. You may want to manually assign the PC's IP address to make it easier to use streaming, but that's not mandatory.