I made sure to search online a boatload, but no results really were as specific as I needed.
First, here's my home network:
(Yes, it looks like a child made it.)
(The '192.168.0.x's mean that the addresses aren't reserved by MAC in the router configuration.)
The 'problem area' is at the bottom right. The CentOS server doesn't have a WiFi adapter, and all I have is an ethernet cable. I plugged the ethernet cable to the CentOS server and the Mac Mini, nearby.
I am aware of the Internet Sharing function but that is not what I need. Internet Sharing gives the CentOS 7 box an IP that doesn't even respect my network's IP configuration (NAT, right?). I need to bridge the connections if possible, kind of like the CentOS 6 VM at the top right. The objective would be for the CentOS 7 server to communicate with the router's DHCP server and get an IP assigned to it and become another member of the network. I would use this server as a home lab, media server, etc.
When I choose to bridge the connections in the System Settings -> Network part, and I bridge the Wi-Fi and the ethernet, after applying the changes, the WiFi immediately disconnects. I searched online and stumbled upon this:
"Note: Network bridging will not work when the physical network device used for bridging is a wireless device. " (https://support.apple.com/kb/PH18510?locale=en_US)
Okay, so unless there's a hacky workaround to this I may need to look for an alternative. I've seen some other answers to similar questions and people just say 'route it' or other stuff but I've no idea how to, especially on Mac. I'm kind of lost and need some straight pointers, really.