Plumbing – Access 2nd-story burst hydronic pipe through ceiling or 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.

You're not going to like the answer, but the way to properly fix this for good is to break up the concrete, cut out and replace the damaged section of pipe.

There are a variety of ways you could break this up. A sledge hammer, a hammer and chisel, a SDS drill with a chisel bit, or a larger chisel like a Brute. If you have a ton of time on your hands, you could use a standard hammer drill and drill tons of little holes around the area to remove and then break it up with a smaller hammer and chisel. The concrete should not crack outside of the immediate area you are working on. As for the pipe, yes you might damage it further but you need to replace a section anyways.

Once repaired you would add new concrete and replace the finish (hard to tell from the pic).

Any other fix is unlikely to be permanent or without compromise.