No USB power adapter, just cable 

Yes, it works with any camera as long as the camera has a external mic input. 

You can control camera shake by using your mirror lock, camera shutter release and cable, tripod securely tightened and all legs as squat as possible. The higher the tripod the less stability you have, but you can always attach your camera bag to hang on the hook, located on the bottom of the tripod to act as a center weight. And lastly, if you do not have a camera shutter release cable, the higher your Shutter Speed the more you will be able to control the “camera shake” or blur in your photos. I hope this helps. 

no it will not the eos-r has a different mount 

As long as the lense is 52mm it will work