Social Authorization is compatiible with virtuemart?
It is combatible with ANY component, that uses Joomla authorization process. As far as I know, Virtuemart does it, so it should be compatible. And if it won't be (which is unlikely), that's not hard to fix and we'll gladly do so, since Virtuemart is a pretty popular component.
Only I would have this request: I would make sure that when one makes the login via social network you create an account for a user in virtuemart so it can proceed with the purchase, your form will allow me?
This might not be required, you know. I never used Virtuemart, but I've seen other e-shops for Joomla and they all have some kind of synchronization. Long story short, if you create account in Joomla, it will be synced with e-shop's database and vice versa. So, I guess, you shoudn't be worried about that.