Capacity expresses the amount something can hold, for example 'The capacity of the stadium is 30,000 viewers', but it's often used in the sense of mental capacity, which seems more similar to ability. They're not exactly the same. For example, in your first sentence, say the job is being a Doctor in a war zone. A trained Doctor would have the ability to do the actual medecine, but might not have the capacity to cope with the war situation. In the second example, breathing capacity is the amount of air the patient can take into their lungs, as opposed to the actual ability to breath. In the third example, I'd say you could probably use either, but people might say capacity because it sounds more formal. Hope that helps :)