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.
Your idea about the 1X6 on either side is a good start. It would give you something to fasten to, in a simple fashion on both sides, although the fastening would be minimal. You may need to increase the number of nails in the jamb to keep it in place over the long haul. Same thing if you use screws.
When the 1x6, for a 6" wall, or if it fits, 1X8 for an 8" wall, is set in place, use construction adhesive between the block and 1X and let it harden. Make sure your block are clean so the glue sticks. This will give a firm base to work to. Do not skimp on the glue. Use a 10 oz tube, a half tube at least, on each side before you set the 1X. Use concrete screws to fasten it in place, they are more reliable for a first time installer. You could use masonry nails but there are places they may not hold. The screws may fail in their holding, but that will be obvious. To increase the chances of holding, use the screws only in the block, not the joints. Keep the screws about an 1 1/4" to 1 1/2 from the edges of the block. The block is thicker there and is far enough from the edge to keep from cracking out (should be). Screws also only affect a small area when they fail, nails break out larger pieces.
To answer the other part of your question, yes you could use framing only on one side, them shimming and fastening the other side is tricky. There are case hardened finish nails to do this, or even screws. For a first timer, what I mention above should do what you need.
Best Answer
Your photo doesn't show much of the area to the left of the opening, but from what is visible, this opening seems a perfect fit for a sliding door. The framing would be above and below the opening, perhaps a stop plate to the right of the PVC, but the door would have a slot to engage the pipe. If extreme sealing is required, weather stripping applied to the stop plate and around the door cut out should give a good closure.
The bottom support framing could contain a long door slide to provide reduced friction, or simply wax the slot in which the door slides and the mating edge of the door. Moisture may come into play if the wood swells after time and should be considered when constructing the assembly.