With that history the primary differential would definately be class III/IV angina. having said that the patient's age would alter that if he was young.
It is usually caused by:
a) A decrease in myocardial blood supply due to increased coronary resistance in large and small coronary arteries. This is commonly due to significant coronary atherosclerotic lesion in the large epicardial coronary arteries with at least a 50% reduction in arterial diameter OR coronary spasm
b)Increased extravascular forces, such as severe LV hypertrophy caused by hypertension, aortic stenosis, or hypertrophic cardiomyopathy, or increased LV diastolic pressures
c)Reduction in the oxygen-carrying capacity of blood, such as elevated carboxyhemoglobin or severe anemia (hemoglobin, <8 g/dL)
Chest radiograph findings are usually normal in patients with angina pectoris. However, they may show cardiomegaly in patients with previous MI, ischemic cardiomyopathy (Dyspnoea largely is a consequence of elevated LV diastolic filling pressures. The elevated LV filling pressures principally are caused by impaired diastolic compliance as a result of marked hypertrophy of the ventricle), pericardial effusion, or acute pulmonary oedema.
Q1. I would say that is pretty much correct, plus preload is increased due to smaller LV chamber size due to the hypertrophy from ischaemic changes.
Q2. Angina can directly cause exertional breathlessness (SOBOE). Other differentials for SOBOE and chest pain would be pulmonary oedema (due to CHF, effusion, infection - though oedema is unlikely to be missed on CXR), pericarditis (more likely to be dyspnoea rather than breathlessness), acid reflux/gastritis (though wouldn't cause enlarged heart and is unlikely to correlate with exercise), pneumothorax (usually more spontaneous and severe - and also persists at rest), pulmonary embolism (as for pneumothorax).
Q3. myocardial ischaemia, due to lack of oxygenation to the tissues of the heart, which is often due to atherosclerosis, but can be due to spasm, anaemia, congenital malformations, etc