Ok . Taking Azithromycin and magnesium should not be a problem. However if you're having diarrhea on the antibiotics that might be more of an issue. I would probably follow up with the doctor prescribing the medicine.
Ok. Diarrhea is a common reaction to Azithromycin but it sounds like you need to be on this medication for treatment of your infection. If you are having so much diarrhea you feel dehydrated, speak with your doctor. It is ok to combine Magnesium Sulfate with azithromycin.
Probably OK. Nuun is not an antacid. It is a sports drink used to rehydrate after strenuous exercise. If you have concerns, why not sip water to keep you hydrated. If diarrhea worsens or is prolonged, see your doctor.