Not every scratch is a polishing job. A scratch you can feel with a fingernail has gone through the clear coat and needs paint.
This page explains the fingernail test, the difference between a polish and a touch-up, and why detailers quote paint work separately from a detail.
Run a fingernail across the scratch at a right angle. If it catches, the scratch has cut through the clear coat into the colour. Polishing such a scratch removes surrounding material to make it less visible, but it does not remove the scratch.
Swirls and light scratches: machine polish. Scratches through the clear coat: touch-up paint or a panel repaint, then polish to blend. Stone chips: touch-up or specialist chip repair, done before a coating so the coating sits on a complete surface.
It removes the material around the scratch so it shows less, but the scratch remains. A scratch you can feel needs paint.
Yes. A coating locks in whatever is underneath, so chips and scratches should be repaired first.