If I were to run a server (lets just say a minecraft server) and no one was connected to it would that still use my Internet download or dose it only use your download when other users are connected to it?

I'm pretty sure any type of server is constantly using your internet connection, regardless of whether or not anyone else is connected to it.

Unless you make a local server, that is. However local servers only let people on your personal home network connect/join the game.

I'm no expert, but I don't think it will be doing anything bandwidth intensive until you actually have people connected to it. However as Spike says, it will be constantly 'using' your internet connection in that it is available for others to connect to, and they obviously won't be able to connect if your internet connection is disconnected.

And the phrase 'use your download' seems a little odd, data will be both uploaded and downloaded (uploaded from the server to the connecting client, and downloaded to the server from the connecting client).

Does this help?

You can also use dynamic dns and forward its port via a virtual server on the router (if the router capable to do it) and the other players had to change their default ('player') name by editing one of the class files with a hex editor inside one of the java archive files. Then it would work in an unofficial way. I played it like this about a year ago with friends, so I don't know what about the latest versions of this game.
Oh, and I think it won't use any download until the router got an incoming packet from the outer dyndns server to let the users through. I still don't know if it works with mobile connections. Cause I assume you'd like to do this via a 3g or 4g modem.