Usually, you would use a sealer to close up the cracks and level out the concrete slab. There are some good Floor Sealers on online flooring stores. Here is a link that might be useful: Sealer

I too have severe asthma and allergies. One source for good information about anything to do with a house and potential problems is the American Lung Association. (For example, after we remodeled some years ago, I had horrible reactions. After six months of increasingly desperate searching for answers, an ALA booklet for health care professionals finally alerted us to the pilot light of our gas stove, of all things.) I too have to stay away from all carpeting. We are currently building a house with all floors in tile or wood for that reason. We recently started looking at vinyl for some of the storage areas, and we have found some fantastic products. I would definitely consider them for a remodel. They are far easier to install than wood, not as costly as wood, they are as easy or even easier to maintain and keep dust-free, and they are easier to redo if down the road and with more time to act, you may want to try for wood. I would check with the ALA about off-gassing of different materials, glues, etc. to make sure your son can tolerate the installation process or how long after installation he may be vulnerable. You have my empathy.

You might start by rolling back the carpet to see if the plywood was attached to the joists. If it has been secured, you will be removing the sheetrock in the garage ceiling, checking on the joists. It sounds like a framing issue. Maybe the joist spacing changed somewhere in the room. Maybe they changed the joist size and used a smaller joist at some point. Ron

If you have a good designer involved with the kitchen, and a good contractor for everything else, it's not an issue. Most floors and ceilings aren't level, even new. Your designer and contractor will handle the details of how to make things work. Basically, you always build in wiggle room. You don't plan things that require tight tolerances. No, 96' is not the minimum allowed ceiling height.