No. Parents often worry about the color of their child's feces. Whereas red and white colored stool certainly requires special attention, yellow, brown, and green ones generally do not. Just be sure your child is getting enough balanced electrolyte drink such as pedialyte not to get dehydrated.
No. If you ask my wife, she'd answer differently, but no, bright green diarrhea is not going to cause any harm. Most diarrhea is viral, and the virus causes inflammation and change to the intestinal world. Normal bacteria there changes. It's that bacteria that changes the stool to different colors, so if you change the bacteria, you change the color. When the virus goes away, it changes back.