Hi Annie;
That is a very nice looking cook stove you have purchased. Unfortunately asking it to run horizontal and heat a mass is most likely to fail.
It will work wonderful for heating your water , cooking on and keeping the room warm. But it must be vented properly or you will have problems.
Trying to slow the exhaust flow will create creosote , this is not good.
Rocket stove's need exact sizing and are run wide open to create the extreme heat that can travel horizontally before rising and leaving the building. That is how they are designed.
Your cook stove is intended to cook on and provide nice room heat. Trying to ask it to perform like a rmh is like asking a VW beetle to compete in an off road rally race with awd turbo Subaru's...
In the future when you build your batchbox you will
experience the incredible roaring fire that is created with Peter Bergs design... there is no comparison to any other wood burner, they are a breed all alone!
Using cement boards or sheet metal to protect the plastic is a good idea.
Adding some brick is OK... adding a lot of brick too near your stove may not be such a good idea.
Metal stoves are designed to shed their heat quickly, they will quickly warp if overheated.
The Axeman fire flue is a really neat product! I have never seen one before. It
should do the job admirably.
Would love to see pictures of your water heating setup after you have it up and running.