Hm. With my login from steam i can't download server, with anonymous i did it.
But, i can't find my server in ingame community tab.
Yes you NEED to download with "login anonymous" you can't use your steamID
If you can connect using "client.connect your.ip.address.here:port" I.E "client.connet 127.0.0.1:28015"
your router needs it's ports opening for rust you need both the server port and rcon/listening ports opened, the Ports used by rust by default i think are 28015 and 28016 you should set your route to open both port UDP NOT TCP
most of the info can be found here http://facepunch.com/showthread.php?t=1414775