Where is best to exercise when breathing very heavily to avoid the risk of lung cancer and what would be harmful to breathe in inside and outside?

Depends: It is good that you are exercising vigorously. Indoors or outdoors may not matter much. If one site has more polluted air, it would be better to avoid that site. Not knowing about the ambient air pollution and indoor air quality where you live, it is not feasible to make a recommendation. For good health - Have a diet rich in fresh vegetables, fruits, whole grains, milk and milk products, nuts, beans, legumes, lentils and small amounts of lean meats. Avoid saturated fats. Drink enough water daily, so that your urine is mostly colorless. Exercise at least 150 minutes/week and increase the intensity of exercise gradually. Do not use tobacco, alcohol, weed or street drugs in any form. Practice safe sex, if you have sex. Get HPV vaccine.