Yes, you can breathe in freefall. When confronted with the sensory intake of a first skydive, many students find themselves holding their breath. Most people do experience some level of anxiety. It is normal to be apprehensive about jumping from an airplane. If you're nervous, tell your instructor and you can work together to work through the fear and decide if skydiving is for you.
Humans instinctually are afraid of heights.
Most people experience some form of vertigo on the edge of a 10-story building, but will not experience the same type of fear from 10,000 feet or higher. The next time you're on an airplane at 30,000', see if it has the same effect as looking out of a tall building window. An individual's safety can be enhanced by exercising proper precautions and procedures. The sport is also referred to as skydiving. USPA has no involvement in the conduct of operations of any skydiving center, parachute center, or drop zone.