This sounds like a good idea actually. Another way to word it would be a "make source code private" option.
Not a bad idea. How it works currently - I believe is that the source is not uploaded when publish is unchecked (just the compiled java bytecode and resources). Would be no difference other than visibility among users (compared to having published the source), to have a "private" option.
I've always just used a flash drive or email for carrying my versions around.
It seems just under half the scenarios on the site have published source code. (number of pages under tag "with-source" compared to number of pages under latest scenarios). So all those without published source code saves decent amount of space.
Guess you could have options for source:
1. Publish
2. Upload (private)
3. Exclude
davmac has a good point, dropbox might be more what you're looking for if you want to access your source in class. On top of that, clicking publish source has no drawbacks really.