Is it possible to change a door handle with a backplate to a door knob without a backplate and not ruin or get a new interior door?

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.

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.

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

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

It’s is possible to remove the backplate, but this will always leave holes that are visible. These can easily be filled and sanded to a great finish. However, if the door is oak veneered this will take considerable skill as the holes may still be on show. Adding a key hole cover where the lock is situated will finish the job off the job to a high standard, these usually match the new knob in style and finish.