I'm a relatively new GM so here's my take on it :
The device could run silent in order to prevent being spotted, although, running silent after being spotted won't change much since you were already spotted. He could use a hide action to try to lose the target that spotted you.
I would allow a rigger to sever his connection to his drone and shut it down from the matrix, but that means you cannot communicate with the device anymore. And be advised, Drones rely on the matrix, if the connection is shut down, how can it return do a designated location?
As for the dog-brain pilot program, I had fun with my rigger :p First time he gave his drone a command to shoot everything on sight, first thing that happened was the drone targeting him. He realized he needs to give precise yet not too complicated commands to his drone. If he were to ask the drone to scan the building, drone would scan everything, carpets, microwaves, lights, posters... etc... he would need to ask to have a blueprint of the building to get what he wants... But that is only my personnal take as a GM.
Hope this helps! I'm sure more experienced GM will provide better tips.