What happens (if anything) to our reputation points when the site becomes "real"? Do we all reset to 0, or is there some sort of grandfathering that takes place?
Whatever rep you gained on the beta site, and badges too, you keep when the site goes live. One notable change is the rep requirement levels for certain actions. The FAQ for the parent site lists these. Note the line above the listing: (note that reputation requirements have been relaxed slightly for the duration of the public beta)
These relaxed requirements are returned to the normal levels after the site launch. So if you were able to, say, view the upvote/upvote values during beta, you may not be able to after beta if you don't have enough rep yet.
This is my experience on the WebApps site, I assume similar things will happen on the others when they leave beta.