Great show
I don't know about stages of cats, but when I finished the quest, my overgrown cat became a 'wiley cat', and I've seen lazy cats, which supposedly are created when you don't train your wiley cat. A lazy cat can supposedly become a wiley cat if you train it again.
Wiley cats also supposedly can catch butterflies and kalphite larvae. (at least that's what the lady said in the quest)
Also, I don't think the cats fight in the rat pits. I think it's just a contest about who's cat can catch more rats first or something stupid.
Oh. And personally the stupidest thing that I've seen in the suggestion forums is that there should be pet dragons. We could fly them around runescape and battle them and stuff, according to the suggestion.
o_o