Network Play System Patching sounds like it's either for some spiffy game to allow network play (if you don't play games over a network just delete it), or, and probably more likely, it's probably some sort of spyware or adware. Do a search on google for "network play system patching" or whatever it's full name is (put the quotation marks in, they tell google to search for that exact phrase), and see what kind of results you get.
That error when you try to uninstall kazaa means that it has already been uninstalled, at least partially. Did you delete the folder for it, or maybe use the uninstaller without going through the "add/remove programs" thing in the control panel?
Firewalls moniter every program that is running on your computer. They also moniter anything coming from the internet onto your computer (downloads) and any connections from your computer sending stuff onto the net (uploads). The only one I have used is called Kerio Personal Firewall, which is free, you can download it from their site. I did not like it. Some programs would not run right with it installed, and it kept crashing. It could have just been the piece of junk computer I had it on though.
I know some of the big name viruscanning software (norton, mcaffee, etc.) come bundled with a firewall. Try going to download.com and doing a search for firewall. You can download free trials, and read what other users think of each program. Good luck!