To find out what version of Ubuntu, try looking under the "System" menu. Is there an "About Ubuntu" entry? Or run "cat /etc/lsb-release" in a terminal window.
The most technical way of finding out your version of Ubuntu (and related distros, like Debian) is to inspect the "/etc/apt/sources.list" file. It's the file that determines where the OS looks for updates.
If your Ubuntu is an old version, like 8.XX or whatever shipped with the Mini, it might be time to consider saving your files and loading a new version from scratch instead of trying to update in place.
As for which Mini you have, look on the bottom sticker. Does it say "1011"? Or input the service tag on Dell's site to look up info. Or run "sudo lshw -C system" in a terminal (= list hardware, just "system" info), it might tell you. Or run "sudo lshw -C cpu" in a terminal. A N270 or N280 CPU in a 10" Mini suggests that you have a 10v/1011.