I do not know how to check disk fragmentation wihout 3rd party tools. I use
http://www.prosofteng.com/products/drive_genius.php, however there are more programs to check disks and fix errors or defragment ones.
Having 15GB left I would be worried of possibility to start loosing files not talking about general computer performance.
if I were in this kind of situation, I would avoid installing any applications being that much limited in disk space. I hope that you have your data backed up. I would use external disk to move important data along with big files (not an applications) to that disk. As well, most probably there are many files that might live on external disks only and be accessed whenever you want by connecting an external storage. In another words, provide more free space on your disk for computer to breath easier. Then install 3rd party disk utility i.e. one I mentioned above and run disk health tests, fragmentation tests and defragment it.
I believe that this not only makes you Mac going to sleep faster but it will improve its general performance as well.
P.S here it seams there is a possibility to get demo version
http://www.apple.com/downloads/macosx/systemdiskutilities/drivegenius.html
it might be that demo still has a possibility to be 100% functional for limited time.
