Look at File > Preferences

You can set the path to the sketchbook folder there...

Tricky.  Presumably that means you also don't have access to:

Documents and Settings -> [username] -> Application Data -> Processing -> preferences.txt

In that case I'd be tempted to ignore the advice given in [Processing installation folder] -> lib -> preferences.txt
and try and edit the path there. 

Alternatively there used to be instructions - IIRC on one of the old forums - on how to run Processing from a USB drive; so there definitely is a way around this issue.

This is still a problem. Unless, of course, I am the only Linux user who wants to install Processing in a global location.

For other Linux users who wish to install Processing in a central location: this worked for me, but it's probably not entirely correct. After you run processing once (and get the error message that lef you to this page), you will have a ~/.processing/ directory. Copy the [install dir]/lib/preferences.txt into ~/.processing/ and edit it. Add the full path to wherever you want your workspace directory to be. Make sure that directory exists or make it. Then run processing. This appears to rewrite the preferences.txt file, but it should work from then on.

No, that's an unrelated issue; it was a bug that was fixed in 2.0b4:

Workaround exists, so no biggie. I downloaded Linux x86_64 on the 21st and got 2.0b3. This thread was the most prominent hit on Google.