Renovating Crawlspace with Poured Concrete Floor
It sounds like you already have a couple of experts working with you. Without seeing the proposed new space, I can only speak to a couple of your concerns. 

There is no easy way to install a sub slab vapor barrier without removing the old slab. You do not want to sandwich plastic between the old and new concrete if you are going to only put in an inch or so of concrete to level the space. I'm sure your contractor will prep the old slab  by cleaning etc to assure a good bond with the new concrete. One or two inches of new concrete should be fine, especially in a space with low, lightweight traffic.  

I see no reason for a drain in this area unless excessive leakage or standing water is a potential problem.

If radon mitigation is required, the collection pipes should be installed under the existing slab via cutting trenches and tied into your venting before you pour the new concrete. Again, your radon contractor who can see the space should be able to advise you properly and make all the connections to your existing system.