1) Can I install Euphony on my Mac Mini? I don't know for sure, but the answer appears to be YES. But, I want to use it in conjunction with Roon with Roon functioning as a Server.
Yes and you can run Roon core.
2) If install Euphony on Mac Mini, how do I boot up the computer? A: I don't know.
For Mac, its better to install bootcamp and go from there. But you can first try to boot off the USB. Press and hold the Option (Alt) key immediately after turning on or restarting your Mac and select the USB drive.
3) Do I uninstall the Roon Core I already have installed on the Mac OS partition and and re-install it on a Euphony partition? A: I don't know.
Euphony is a complete OS made out of ArchLinux. You would install Euphony directly on a Boot device, like you would do with OSX.
4) How do I specifically use Euphony with Roon as a server and send the music to an endpoint renderer? A: I don't know.
In Euphony you can select which audio player you want. When you select Roon, you go into Roon's setting to configure your endpoint.
I hope that helps.