It's literally the second hardest thing to do after the biking/running/swimming/skiing itself. Fueling is the operational excellence challenge of endurance sports.
It does. Getting your stomach good at that (and figuring out what food you can personally tolerate best) is a nontrivial part of training for longer ultramarathons.
Breaking down fat costs a lot of oxygen. The body can run on fat if you have a lot of oxygen to spare. If the effort is causing you to breath heavily, then you are probably mostly burning faster carbohydrates (glycogen, a sort of sugary fuel the body has already stored in the muscles).
Running out of fast carbohydrates is (at least in biking) called "bonking". You'll feel extremely tired, maybe be shaking, and feeling dizzy. It's a blood sugar dip: a very low and long dip. Your brain usually runs on sugar too, so you'll feel stupid and angry. Your body still has fat stores, so your body can keep running - but at a much lower effort intensity.