Congratulations! In answer to your questions:
1. Usually one hand if I'm on a smooth surface. Always two if I'm near traffic or on a rough patch of trail.
2. Locked, but my BOB doesn't have a swivel option.
3. It was an adjustment, but I'd say by the third or fourth run it was beginning to feel more comfortable. We started at 30 minutes (4 miles) and worked our way up to more than an hour (10+ miles).
4. I usually do normal runs at 6:45-7:10 pace. With the stroller it can range from 7:15 to 8:00. I try to keep the effort consistent and not worry too much about the pace or distance since I only do easy runs with my daughter.
5. No hamstring issues, but I have to hunch a bit since the handlebar is so low on my stroller.
Enjoy your runs together! One thing I've found as she has gotten older is that it's a good idea to stay close to home or near a park. That way, if she gets cranky, I can get home quickly or take her out of the stroller and let her play.