Can prednisone, do the exact same function that cortisol do in the body\like give me back my ability to exercise easier\? If not what is the treatment?

No. Prednisone is an antiinflammatory corticosteroid and is not meant to replace cortisone deficiency in our body. Cortisone acetate is what is used for that purpose such as in addison's disease or adrenal gland insufficiency.
Hard to say. Prednisone is similar to cortisol in its anti-inflammatory effect. Oral treatment disperses through all body tissues and for some conditions this is a good thing. Its wide dispersal also increases chances for long term side effects.Targeted use as an injection near a problem site is preferable to oral meds. How to rx your issues should be based on proper history and m physical exam.