Running everything via docker solves both problems no matter which OS you choose since the underlying OS doesn’t matter.
Yes, but also no.
Long story short: you can’t run Windows containers on Linux. And to run Linux containers on Windows requires essentially running Linux on Windows, and then the Docker engine on Linux. (See also: running Linux containers on OS X.)
There do exist multi-arch container images, but that’s the result of proper planning. One example: https://hub.docker.com/_/hello-world
More info: https://hackernoon.com/how-to-run-docker-linux-containers-natively-on-windows-ti1i3uxr
I’ve got Plex running on 2 non-Windows systems: Raspberry Pi (Linux Docker container) and TrueNAS (FreeBSD jail). No issues.
If I could suggest something…
Try setting up a Linux VM on Windows. I’m not a Windows guy, so you might need to research how to do this. My go-to would be VirtualBox; I don’t know if Hyper-V supports non-Windows VMs, and I’m not intimately familiar with setting up WSL.
Going the VM route will let you kick the Linux tires without committing to more hardware. Or, you could get a Raspberry Pi. External USB drive optional, since you should be able to configure Windows to share your library over the network and just have your Pi mount it.