Thats how they work, the same as you hand sharpen a drill bit. You shouldn't sharpen on the side though.
That'd be like pushing the end of a bit of wood into saw-blades without using a table/bed. Ya don't angle up against a downward wheel at those speeds.
Plenty. Safely. Considering what they are used for, burrs are not a consideration, so sharpening forward not a worry.
All I can say is that in all my years I have never seen anybody sharpening a drill in the manner you have said and would consider your method to be more dangerous.
****. (For heaven's sake)You should not be holding a piece in the air and chucking a fast grinder wheel at it. Heck, they even have tables for you to support your stuff. You don't lean a drill against a table and point it upwards. I can see now why I've still got all my fingers!