I would like to know either (a) what animal(s) is/are most efficient in extracting energy or calories from food, (b) how one would go about finding an answer to that question, (c) the terminology one would use to search the literature for an answer to the question.

Regarding (a), I've been considering cows or camels at least somewhat inefficient because their feces and be dried and burned (hence the animal does not convert all the energy in its food to energy for its own use); it is likewise with whales, the evidence being that other creatures feed on their excrement. I assume all animals have guts inefficient to some extent but would like to know how animals rank.

Regarding (b), my guesses include subtracting calories in excrement from calories in food or, perhaps, comparing weight of food and weight of excrement (as I have seen done with coproliths).

Regarding (c), as I have never studied any field of biology, I do not know what terms would be applicable ("metabolic efficiency"?) or even what specialty would be relevant to such a question.

I would have thought the sorts of animals you should be thinking about are the small rodents and gerbils that live in the sahara and gobi deserts. I think they reabsorb almost all water and pass tiny amounts of faeces. I doubt there will be much if any literature published on this as a specific field.

Regarding literature searches, the best magic words I can come up with are "digestive efficiency". You can combine this with "animal", "vertebrate", or the name of any specific animal group you may be curious about. There does seem to be a fairly substantial literature on the subject, but I don't know it particularly well as I'm not a physiologist.

One complication to keep in mind is that the ability of an animal to extract energy from its food is partly a function of the food, as opposed to the animal. Cellulose is notoriously hard to digest, even with the help of symbiotic microbes, so some herbivores have evolved special tricks for extracting as much energy as possible from plant materials like leaves and grass - anything from ingesting their own faeces for a second round of digestion to having a multichambered stomach, or just a very large set of intestines. However, comparisons of efficiency between animals with very different diets are not really "fair". Comparing apples and oranges might actually be reasonable in this context, but comparing fruit of any kind to either meat or leaves would be more dubious.