So what the Fuck is the cat supposed to be. After reaching the end with my second character, I decided I might as well kill everyone before I move on, only the cat is bleedin' invulnerable, and is well aware of that fact given how she goades you on to try attacking her again.
I figure she's apart of the same talking cat race as the one from the first Dark Souls that was buddies with Artorias, though you could at least kill her... right? Actually doesn't she vanish after you've attacked her? In any case the cat in DkS2 is clearly wise and all knowing and all that, so she's undoubtedly been around for some time. Probably just a mystery for a mystery's sake?
There's some pretty convincing speculation that she's Alvina.
And you're right, she does know a lot more than she's letting on; or seems like it anyhow. She has some interesting dialogue for you after you beat certain bosses and she is the only character (aside from the Emerald Herald) to actively discuss you becoming the new Monarch and taking the true throne.
And no, Alvina couldn't be killed in Dark Souls 1.
I'm pretty sure that description is in fact from the cat ring she sells you, though I assumed it was to imply that the cats eventually turn into the rings--by way of their essence/spirit/soul/othersuchmojo transferring or what have you--once their 'time is up'.