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For 1 it really depends on what you want to do. My guess is that 1) is going to be easiest with both running on the same machine.

For 2 groovy is more mature and has more capabilities. However if hydro has the feature set you want released then it's going to be slightly newer and more up to date.

For 3 Gazebo is very closely integrated with ROS and I believe the majority of users use it with ROS.