Concrete – Pouring concrete for an under porch crawl space

Yes, bringing the crawl space into the conditioned space is generally recommended as a way to prevent crawlspace moisture problems (I assume this is what you mean by encapsulate).

This means:

1. sealing vents to the exterior
2. sealing the dirt floor with polyethylene sheeting (at least 6 mil), or concrete
3. creating vents between the living space and the crawlspace (ideally supply air to/from the space with HVAC ductwork), and
4. insulating the interior side of the crawlspace walls on (not necessary in climate zone 1 or 2; and preferably with board foam or spray foam because fiberglass doesn't do well with moisture).
5. probably a good idea to remove existing floor insulation

This will prevent humid outside air from coming into the crawlspace and condensing on cold surfaces, and prevent/reduce moisture from coming up through the dirt floor or walls. Your AC will also deliver cold air more effectively. Good site drainage is also key.

There are many good references on how to do this properly:

http://www.housingzone.com/crawlspaces-vent-or-not-vent

https://buildingscience.com/documents/bareports/ba-0401-conditioned-crawlspace-construction-performance-and-codes

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.