Rear end questions - rebulid

You could, but don't have to clean the inside of the tubes. So long as there not exposed to water for any length of time creating that nasty goo that oil and water create after sitting for a while.

Just clean up the outsides of the grease and etc.... install the center section and fill with dino oil until it drips out of the upper hole that you use to fill it. No need to spray anything on it.
Your good to go. Drive away slowly and slowly accel to the roads speed limit. No need to get on it right there and then. You could just drive to the Hwy and see how you like it. It'll be fine.