The avatar parameters are stored in cookies and sessions. That's about all that's saved, because it's all I need.
At some point in the future, there might be a gallery of previously generated avatars, but they won't be connected to the visitor who made them.
Avatars In Pixels uses Google Analytics for statistics (because I'm curious), and Google Adsense for ads (because I like money).
Both collect information and have policies that you can probably find through googling, like: