By removing the backplate your left with the fixing holes to repair, which would be a minor repair with the appropriate filler. If a key hole is also cut then use a keyhole cover to improve the appearance with the new door knob.

depends if the plates for a key (to hide hole) if not it should be fine

yes, this is possibl, if the door is stained just use a litle wood filler, that resembles the same colour as the door, you won't get it exact but not far off and if your door is white then just fill with any filler and repaint.

Removal of backplate generally leaves holes imperfections however these can be filled using a two pack wood filler and sanding off prior to the finish