To remove fake nails without damaging them or your natural nails first apply some petroleum jelly to the cuticles and the skin around the cuticles.
Then take some acetone nail polish remover and pour the acetone nail polish remover into a glass bowl and then soak the nails in the acetone for 20 minutes.
After soaking the fake nails into the acetone the fake nails should come off easily without damaging the nails or your natural nails.
If not you need to soak the fake nails a little longer and try removing them again.