You can't really feed them in the fridge- they go dormant. To feed them you will need to take them out and put them in another container at room temperature. My colonies are now self sustaining, and I use 3 gallon rubbermaid storage containers. Each container can hold many 10s of thousands of mealworms- when I was starting them I stocked them with 5,000, and after several months I had zillions of babies in there. I sort the beetles into new containers as I feed out- just like I do my roaches to start new colonies.
You can feed mealworms a mix of about any sort of dry stuff you would feed roaches or crickets to gutload them, and gutloading significantly improves their nutritional value, just as it does for roaches or crickets. For my colonies, I base my mix with ground up grains (whole wheat flour, corn meal) and add other stuff to that (literally anything I think at the time that looks like a "good idea" including stuff like spirulina, bee pollen, dried ground up vegetables like carrots, bell peppers, tomatoes etc). Literally anything that is dry that is found in cricket gutloads or roach gutloads can be offered to them.
I grind everything into a powder so I can sort through to collect my mealworms and beetles with a screen strainer when it is time to feed. Makes collecting a couple thousand reasonably quick and easy enough.
But you cannot feed as much of the "wet" fresh veggies and fruits- they achieve too much dampness more easily than roaches or crickets, and dampness will lead to mold and/or tiny mites.
Probably straight from the insect farm to your fridge, they are much poorer nutritionally. Most likely they have been fed corn meal or some other combination of simple grains and little else.
Probably- I don't know that for sure, but seems logical that insect farms would use the least expensive food items to raise their insects (including crickets- I'm don't mean to pick on mealworms here).