I've never heard that the magnetic field on clip-on sunglasses is harmful to the eyes or brain, but I've heard magnets may interfere with pacemakers. So you should consult your doctor before buying magnetic clip ons.
No, clip on sunglasses won't cause any damages to your eyes if you use them properly. Clip-on sunglasses are made to help people correct vision and prevent UV rays and intensive light. And they are very convenient. When you stay in the sun, you can take on the clip-ons to shield the eyes. And when you in room, you can take off the clip-ons and use the clip-on sunglasses as a pair of Regular glasses. As long as you wear accurate prescription lenses, the clip-on sunglasses won't cause any damages to you