This is the first time I'm seeing IPFS. So when the IPFS servers are running, they register themselves with some central node to let everyone know they exist/are online? This is how they get away without a static IP address? Am I thinking about this correctly?
No, IPFS uses a distributed hash table to find content and nodes on the network. The only centralised servers are the gateways between the regular Internet and IPFS, due to necessity. However it is possible to run your own gateway, and many do.