Is it possible to back up in-app purchases and game saves?

Solution 1:

Normally apps that sell in-app-unlocks (as apposed to like packs of currency or the like) will have a button to restore purchases. This will give you the unlock again after it checks your account.

It is dependant on the app though. IF the game has login system with a username and password etc, then it may keep track of the purchase from your login information.