There is no easy set answer to your questions. There are all kinds of variables including past injuries that can contribute to how far you can push it. I will lay the basics down as clearly as possible.
- Running is an aerobic exercise, The link attached is some solid information on training to a target heart rate which is measured in beats per minute. Basically you will choose a baseline from your resting heart rate and use cyclical training methods to control your heart rate by alternating Work and Rest intervals- which it sounds like you are already doing in some version.
- you asked if the stamina problems you are seeing are due to cardio or lung capacity. Those two Items are directly linked and will both build over time.
- yes you can keep pushing through without causing yourself severe bodily harm.
- As to learning and improving your form I would suggest a running forum to find a partner in your area or even a personal coach, maybe the local high school's track coach would be willing to help out for a boosters donation? You just never know until you ask.
_ As a side note I remember your previous post about reinlisting and do not recall what you choose to do or if you even posted your final decision but Most recruiting offices will help a recruit prepare for physical fitness requirements.