The only thing I really don't agree with is any possibility of Varys being a warg. It's just smacks of reaching for crazy theories for the sake of reaching for crazy theories. Your Varys as Faceless Man theory has merit. Varys as warg really has none. It's just too easy to start super powers on every cool character. This, to me, is like saying Mel is going to resurrect Jon just because we saw another Red Priest with the same power. Everyone has their strengths and weaknesses and I respect GRRM's vision enough to think that he'll separate them a bit and not just hand out special abilities to everyone because it makes things easier to explain.
Back to wargs: For the purposes of this series, that's really a Stark thing. Sure, Varamyr was a warg but the entire reason for his existence as a character was basically as a warg handbook for the reader so that we can better understand what's up with the Stark children. Also, I doubt anyone outside of the North could even be warg candidate. The Faceless Men don't even seem to know of them as demonstrated by Arya being able to use it against the Kindly Man without him figuring it out.
Finally, that cat is Rhaenys' cat. She named him Balerion. Of course, that's just a theory but it's something I picked up on years ago on my first re-read. Later I found out that many other people also picked up on it. I don't know what that will mean to your theories and what not but hopefully it helps you put more pieces together! Here's a wiki page about it:
http://awoiaf.westeros.org/index.php/Balerion_(cat)