As for your first question, you might be interested in a program called "screen" which will let you detach the program that is running from the console and then disconnect. When you reconnect you simply have to issue a command to reconnect that process to the console and voila, it's back still running just like you left it. =)
As for your second question, just open up an xterm and type "df" at the prompt to see how much space you have left on your drives.
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