Rabbit starvation, more formally protein poisoning, is what happens when someone eats a large amount of extremely lean meat and almost nothing else. Rabbit is the classic example because it carries so little fat that the body cannot get enough energy from it, and there is a ceiling on how much protein the liver can process into urea safely. The result is that people eat more and more, feel worse and worse, and develop diarrhoea, headache, fatigue and weakness while technically eating plenty. Arctic explorers and trappers described it repeatedly. Adding any fat or carbohydrate to the diet resolves it, which is why it never occurs in ordinary eating.

No. Fresh rabbit is graded clean on both histamine content and histamine liberation, which makes it one of the safer choices on a low histamine diet. The caveats are handling rather than the animal: wild rabbit that has been hung as game has been aged on purpose, and any meat that sits in the fridge for days accumulates amines. Buy it fresh, cook it, and freeze what you do not eat.

Yes. Like all plain meat, rabbit contains no fermentable carbohydrate, so portion size is not a FODMAP question at all. If a rabbit dish upsets your gut, look at the braise: onion, garlic, cider, prunes and mustard all appear in traditional rabbit cooking and all of them have FODMAP or other trigger loads.

In practice yes, and that is why almost every traditional rabbit recipe wraps it in bacon, bathes it in cream or cooks it in oil. Rabbit carries only a few grams of fat per hundred grams, which makes it dry on its own and, at the extreme, is what produces rabbit starvation. For a normal meal you simply need a fat source and a carbohydrate alongside it, which any ordinary plate already has.