Here are two solutions that this could be,One is a belt broke in a tire,usually a front tire and it will seem like a wobble when braking to stop. The other is the front brake rotors out of round and usually you can feel the brake pedal pulsating a little when breaking to a stop.
Yes your rotors are warped.
Odds are the shaking when braking (no pun intended) is due to "hot spots" on your front rotors. If they aren't too thin, they can be turned and probably eliminate the problem. I think I'd replace the pads, even if they look good, just to have a fresh start on the front brakes.
As to the engine light coming on, I'm pretty sure there is no connection. Take the car to a auto parts store and see if they can do a free check of the "check engine" light.
Good luck!
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