Autonomous Quadcopter power distribution and sensing concerns
Your question is quite long. I've broken it up into several parts:


  whether or not it is safe to have a common ground on arduino with an 8 amp power supply 


Yes. In fact, if you have any electrical connection (even a signal) between those two, you'll need a common ground to ensure integrity of the data being sent.


  if it is safe to use a 5 volt 8 amp power supply with these sensors.


I didn't see how much they drew. Without a lot of information, I'm going to say yes. If you don't need that much current, consider removing one of them so you only have 6A or 4A, since 8A is quite a bit if you aren't using it (and you might waste electricity in the conversion process). Make sure to have a thick enough wire for it. A best practice scenario would be to use each ESC separately or use two of the ESCs in parallel (with all  of the grounds connected!). This would isolate the current to either 4A or 2A.


  while powering my IMU off the BEC and sending motor PWM signals my sketch would run for about 10 seconds then freeze. It was not until i powered my IMU off the arduinos 5 volt power that I was able to run the sketch flawlessly. What could have been causing that?


I'm not quite sure what would be causing that without seeing the code/circuit for that. The only thing I can think of is the grounds weren't connected and the signal got corrupted.