Hey there! Lots of questions. Hopefully I can answer them all, but let me know if you need anything else.
1) JFBConnect supports multiple profile extensions for Joomla to store the user's profile data into. JFBConnect doesn't hold the data itself; we don't create a profile extension. There's lots of great ones already out there that have their own integration into many other extensions. JFBConnect currently supports EasySocial, JomSocial, Community Builder, Kunena, K2, Virtuemart, Hikashop and a few others for storing data. We also have a "Custom Database" plugin where you can store profile data in any database table you want.
Unfortunately, though, Facebook doesn't let us obtain the phone number from a user's profile. That's never accessible anywhere within Facebook for obvious privacy and security reasons.
2) JFBConnect wouldn't directly. However, we can store the user's avatar in any of the profile extensions we already support. Many of those extensions already integrate with Zoo and should be able to display the avatar that JFBConnect downloads within Zoo.
3) This isn't something we support directly. We do support Open Graph Actions, which get posted back to a user's Activity Feed in Facebook. However, we don't support purchases within Zoo cart right now. You'd likely need a developer to help you implement this if it's necessary. I'd also recommend ensuring that your users would want their purchase activity automatically posted to their timeline.
Instead, you may want to consider a simple Like or Share button on the purchase confirmation page so that the user can choose to share your site.
I hope that helps,
Alex