Is there any way that I can tell what my quality rating is on Limewire?

Yes, there's a description of how it works somewhere in the source code...

go to www.limewire.org

I suppose you could name a file some strange name, put it in your shared library, then do a search for it.

I haven't figured out yet if my own libraries show up on my searches, but that would pretty much show us the answer. Tell us what you find.