You could run when you wear the contact lenses. However it is bad for your eyes because the air stream will make your eyes dry. The dryness of the eyes will make your eyes get infection easily. You'd better not wear the contact lenses when you run. The sweat from the head may come into the eyes and make your eyes become painful. The invisible bacterium may come into your eyes. The active exercise may let your eyes become red. You'd better not wear the contact lenses and do the running exercises. If you have to do for the convenience, you could wear the band on the head to avoid the coming sweat.
It depends. Some people feel uncomfortable when ruining with contact lenses. But it is OK for me. I often wear my contact lenses when i run. And the contact lenses won't affect me but give me clear vision. I think it is more convenient than wearing eyeglasses when running. You know, when run with eyeglasses, the eyeglasses may slip down your nose, that make really bad during running. But the contact lenses won't meet such problem. So, you can just have a try, or consult a eye doctor in case.
I think you must be one of those sports fans right? Actually, I used to have the same question but later I realized that it would be absolutely ok for anyone of us to take exercise or jog with a pair of contact lenses in, those contact lenses would not fall out easily. So you don't have to worry, just enjoy your sports hour. But try not to get too much exercise, which would be bad for your eye health.