Power line ethernet has its uses but it's limited to hardware that is on the same circuit with each hardware being plugged into proper power outlets without any extension leads, switches, circuit breakers or safety devices between them.
Yup. Much better run a Wireless bridge if the distance is not too great inside a house.
I actually have here a few Netgear Powerline Nano 500 kits that I was sent for eval last year. Huge PoS. In my house it goes from 105MB/s at the router on my 2nd floor to 1.8-3Mb at the receiver in the basement, and sometimes it even disconnects.
No Surgeprotectors plugged in or anything. If you have a house-wide UPS system also, forget about using it.
YRMV though.
Can you just run cat 6 to the outside from the current set up. drill out seal it with silicone to keep bugs and water out go back in to the garage wherever it is convenient. Set up an unmanaged switch and be up at a low cost? 800 to 600 RPM upblast exhaust fan for the garage may need additional cooling past that. Would be less then $500 if you can get a refurbished fan someplace.