[MunchkinMan]

All of your questions are answered by the following statement: The Doppleganger is your exact copy, and gives you a bonus that mirrors your current combat strength. That means any change to you will be reflected by your Doppleganger. And, since it's a bonus, you can't use it to get an extra Level from Pukachu. And, since it's an Item providing a combat bonus, a Thief can't backstab it.