Is there 12" between the ground and the bottom of any beam, as per code?
Or, 18" to the bottom of the floor joists?
Pic. #1 - should be a weatherstripped door with a sealing threshold. Preferably insulated as well. Is the idea of a cold room with slats in the floor for storing your own food, potatoes, carrots, etc.?
Pic. #2-- interior finish should be more than fire-taped drywall, which will mold, if needed as a "cold" room.
Pic. #3--- Yes the vapor barrier should be taped to the concrete wall and foam board added where missing. Also tape the seams of the board. That duct patch is terrible, duct tape as shown has a four year life. (Not counting the cardboard ? patch). I doubt it is for heating the crawl, more like a mistake and ran a duct above instead. (It looks a lot bigger hole than needed?)
The foam board should be blue to stop moisture, not white. http://www.energysavers.gov/your_hom.../mytopic=11620
And it may need to be covered, per code: http://www2.iccsafe.org/cs/committee...E_06_64_07.pdf
Because of these characteristics, foams used for construction require a covering as a fire barrier. One half-inch thick (1.27 cm) gypsum wallboard is one of the most common fire barriers. Some building codes, however, do not require an additional fire barrier for certain metal-faced, laminated foam products. Check with your local building code/fire officials and insurers for specific information on what is permitted in your area.
Be safe, Gary