Not for mountain biking, but you can definitely bike around the park and around the mountain.
This is an old question, but I wanted to add a few things. There are no trails in the park to ride on-bicyclists must stay on the roads, and no sidewalks either. The dirt trails in the park are for "feet" only, no bicycles. As for outside the park, there is the Stone Mountain Trail that starts inside the park and ends at Centennial Olympic Park in Downtown Atlanta. It is paved and almost 20 miles long.
Yes. Their bike trails are very popular. Enjoy.
Yes around the mountain and throughout the park. Not allowed on mountain. Beautiful scenery... Segway tours also.
No
Ditto the previous answers
There are bike lanes around the mountain. I've seen a lot of bike groups ride together.
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