Sphere games can technically do anything at all with networking. The sockets exposed are BSD sockets, which are what you'd use in C or C++ to do it.I have personally made a couple networked tech demos and an IRC client using Sphere. I can tell you from experience that it works just fine for server/host configurations, hosting games from Sphere, or connecting to the internet. If you wanted to do MySQL, you'd need to emulate the entire protocol. An IRC client is simple to implement, and is a good way to get your feet wet with networking, while still producing real, usable things.
BSD sockets is a way to read and write data from a network. If you know about C-style file handles, they work like that. Which, coincidentally, is pretty much exactly how Sphere's rawfiles work.MySQL is higher level. It is (correct me if I'm wrong, I don't know that much about databases) an implementation of the SQL database programming, and a database backend.You'd send MySQL queries over a network. It's the data you'd send and receive. You'd use BSD sockets to specify where and how to send it, and to actually read and write that raw data to the network.To make an analogy: think of MySQL like a file format, and BSD sockets like what you'd use to actually read and write data, any data, to a file.
The port-forwarding, floating IP, and telling users your server IP isn't really a Sphere-specific issue--though you would have to deal with it if you wanted to host a Sphere-based MMO. For instance, that is how a lot of MineCraft servers work, since there is no first-party hosting and a lot of independent, privately owned servers.The beauty of using BSD sockets, though, is that it would be simple to write the server software in another language and have it work fine with Sphere.
While Sphere has decent networking support, it's not that good for MMO's. Also you need to port forward and send IP addresses and stuff to get a game between two others. I once had a networked sphere game with 7 people online. But it was only for one day, and my IP address floats so I couldn't keep a persistent game running 24/7 without a real server to run it on.Then if you had a real server, Sphere itself was designed for games. So unless you write a server in another language, you can't have it handle a high throughput.In short, Sphere's networking was designed for LAN play, ideally.
I assumed servers have their own OSes and programs and stuff.
I don't know a lot about it, but you might be able to use a server emulator like Hamachi, which should take care of the IP and floating and stuff problems. I know people use it to host small Minecraft servers for their friends without actually owning any server equipment.