You are misunderstanding many things.
A round in boxing and other sports last 3 minutes. In real life, a violent encounter lasts about 7 seconds. If you are out of breath, it is because you were wasting your energy in unnecessary motions and you were not breathing properly in addition to being out of shape. The first two you have to workout yourself. As for getting in shape - jump rope. Shoot for being able to do it for 3 full minutes.
Balance: while leg strength helps, most people who are off balance are that way because of improper stance. You need to practice your forms with an eye towards doing the stance properly. You also need to focus on the transition from one stance to another while staying in balance - this is call "dynamic balance". You should practice your techniques as slow as possible and see that at very point of your moves, you remain in balance. I suspect you have been doing it wrong for a long while and just never noticed it because you were doing it fast.
Flexibility: stretch. Do it regularly AND properly.
Reflex: reflex is not going to come easy. It is a combination of mind and body working in unison. The mind has to be clear and uncluttered while the body has to be tension free. You also need many hours and countless days of practicing a motion over and over to develop reflex. And those motions have better be right because if you do them wrong, you will be doing it wrong as a reflex. This is not something anyone is going to be able to help you with on the Internet. It takes both dedication AND guidance from a good teacher.
You sound like a very responsible young man, so here is the one rule that you should following in your desire to improve. ALWAYS do things right. Doing something correct and right is more important than doing them many times or many time fast. Someone who practice 2.5 hours a week, but does everything as near to perfection as he can will progress faster than someone who practice 10 hours a week but with no focus on correctness. Go for quality of training and not just quantity.