Is a mrsa uti infection contagious to others by airborne bacteria emanating from the patient by them coughing, etc?

Maybe, not airborne: When someone has a staph infection (MRSA or not), other people in the same household often are at somewhat increased risk. It's not so much airborne, but from skin surfaces, which typically are contaminated with staph no matter where the main infection is; and from skin, household dust and surfaces often are contaminated. Common sense hygiene (hand washing) and housecleaning help reduce any risk.

No: MRSA may be present on the skin or in the nose of otherwise healthy people. 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.