Babies must pass that black stool called Meconium within the first 24 hours of life.

Kindly follow your doctor's prescription and do not self-medicate. Flagyl is an antibiotic and constant exposure can lead to antibiotics resistance.
Moreover, some diarrhea is not a bacterial infection that can be treated by antibiotics.

Because he knows better. Sometimes, the doctor prescribes a drug based on the health history of your baby :)

Teething has got no connection with the stool.