I was taught to breathe inhaling through the nose, holding the air very low into the abdomen, then exhaling. It is forbidden to breathe through the mouth, it doesn't matter how tired you are, you will be hit with a staff if you breathe through your mouth.
It is the foundation of every thing we do. My master says "Everybody must breathe to live, however one of the most difficult things to learn is how to breathe properly". It takes years to understand, develop and ultimately, to feel it.
I was taught Ki-Hap is made to channel the energy from you to your target. It is an act of focusing your very being (your spirit) gathering the energy from the low abdomen, holding it until your movement finishes, then releasing it using your body as a conduit for the energy. Both the release of the Ki-Hap and the end of the movement (kick, punch, etc) must coincide very precisely.
One of the first things I learned was "Ki-hap is not made with the throat" it is not a yell, it is something more profound.
On the belt tests, all hyungs must have a proper balance of breathing, ki-hap, strength, speed and proper execution.