Please tell me if oils like mineral oil on skin are safe and if they can have any side effects?

Safe. Contrary to what you may have read on-line, mineral oil is pretty harmless. If you apply it right after showering, while your skin is still moist, it will seal in the moisture and relieve dryness. If you have very sensitive skin you might get pimples or bumps from plugged up oil glands - but you won't know unless you try it.