I'm not sure about the leaving transparent sections uncropped, but the origin points really change. It happens to me as well as everybody. Technically, the hotspots don't change their position at all. It's the image of the sprite that changes position when cropped that forces us to have to readjust the hotspots for every frame. I would suggest you find a software specifically for making animated GIFs (with transparent background) and animate/crop your sprites there and just import the animated GIF in C2 then set the hotspots just once, apply to all frames.
edit: try clicking crop 2-3 times, or you might be referring to transparent sections that really can't be cropped (because C2 just crops your image to the smallest possible containing rectangle). If you make a diagonal line, it will leave a lot of transparent areas because C2 can't crop your image (diagonal line)