a) all calories in the food you put in your mouth are digested;

This is certainly not true. Usually calories in food are measured burning the stuff and measuring the calories emitted, but of course our digestive tract doesn't work like that. This means that we always absorb less calories that are in the food, indeed cooking was a great revolution in human history because it allowed more calories to be extracted from the same amount of food.

b) the digested calories are either stored as fat or spent as work; there is nothing else that could happen with them;

This, on the other hand and with the caveat of a), seems pretty uncontroversial. There are different deposits of long-term energy, such as glycogen in the liver, glycogen in the muscles and adipose tissue. But other than accumulating or being used to produce ATP, I have never seen any reason to believe that calories are used for something else.

c) the calories are the whole story about nutrition and metabolism, and all calories are fungible.

Well, this is obviously untrue, but usually "calories in, calories out" is used in the context of weight loss.

Could it be that some people are forced to eat large amounts of food just to extract the right amount of vitamins and minerals, and any attempt to eat less will lead to symptoms of malnutrition?

It can be, but the body is usually extremely efficient when extracting vitamins out of food. An inability to do that would be a serious business, most probably caused by a genetic disease, and surely cured by supplementation rather than eating large quantity of food.

maybe you cannot always get thin by eating less calories than you spend working; but if you eat more calories than you spend working, you will inevitably get fat.

I don't see how the first sentence would work. As far as I know, there are no hidden reserve of energy besides glicogen, muscle proteins and fat.

But it is possible that some of the "calories in (the mouth)" may pass through the digestive system undigested and later excreted? Could people differ in this aspect, perhaps because of their gut flora?

This is a certainty. Think for example to all the calories contained in indigestible fibers.

Also, what if some people burn the stored fat in ways we would not intuitively recognize as work? For example, what if some people simply dress less warmly, and spend more calories heating up their bodies? Are there other such non-work ways of spending calories?

That is called non-exercise activity thermogenesis (NEAT) and is the way that most of our calories are expended: keeping body temperature constant, providing energy to all the chemical reaction in the body, etc.

While reality seems to suggest that most people, both thin and fat, keep their weight stable around some specific value.

Yes, there is a set-point which is regulated by a complex interaction between various hormones, such as ghrelin, leptin, insulin, etc.