Open Source Shareware? I've never heard of such a thing and limewire.com

Linux

https://www.redhat.com/apps/commerce

If it's open source, how can one attempt to charge for a 'pro' version?

1) OpenSource doesn't mean something is free at all (neither as in "free beer" nor "free speech")
2) And GPL'd doesn't mean something is free like free beer either: http://www.gnu.org/philosophy/free-sw.html

If I download the source code from the website and help in development, will my work profit somebody else?

Yes. Everybody will profit from your work including yourself.

Where do the funds go, anyway?

They pay their bills and...

http://www.limewire.org/wishlist.shtml
http://www.limewire.org/awards.shtml

Is the 'pro' code not gpl licensed?

Right and again, GPL'd doesn't mean something is free like free beer. http://www.gnu.org/philosophy/free-sw.html

I think it is OK if I say "we" the Open Source devs (see LW's about box) of LimeWire are quite happy with the current model. We have the freedom to do whatever we want (as long as we don't violate the GPL or harm the network), they benefit from our ideas+impulses and in return they give us access to a professionally managed code base (which has the value of gold and I appreciate it).