There is a text book answer for each of the above, but in my experience the actual death temp depends on several complex variables including soil nutrients, plant health, water absorption in the plants, and length of time at the low temp. Hence, in my opinion, there is no absolute one answer to the question.
Soil Nutrients: Without question, plants grown in highly nutrient dense soil are more tolerant of low temps. I have seen synthetically fertilized plants consistently expire at higher low temps than naturally fertilized plants.
Plant Health: Plants that have been weakened by insect damage and/or disease(sometimes unseen) are much more susceptible to damage/death from low temps. This factor alone can make a difference of several degrees in the low temp tolerance.
Water : Plants that are high in water absorption do better than otherwise, especially in temps in the 20s. Temps in the teens, it may not be as much a factor.
Time : 15 deg. F low temp for an hour before sunrise is no comparison to all night at that temp in the amount of damage it does to the plants.
Further I have observed that some plants started from seed in the ground rather than started elsewhere and transplanted do much better at low temps. Onions are a good example of this.
Because of the complex set of variables there is no one answer for each plant. Here is my own garden experience for each plant mentioned by the Op (all temps in F):
Broccoli: damage at 22 deg. and death below 19 degs.
Cauliflower: damage at 31 deg. and death below 27 deg.
Cabbage: damage at 20 degs. and death below 12 degs.
Carrots: damage at 20 degs and death below 14 degs.
Romaine : Damage below 24 degs. and death below 19 degs.
Another I have years of experience with are onions. I have had onions take about 50% loss at 10 degs that were started from seed. Transplants 50% loss at about 15 degs.