what causes grooves in brake rotors?

Normally those are from debris that got into the blend of friction material that is used to make the pads, or from something like a stone or piece of steel that got stuck between a pad and rotor. The vehicle shaking won't be from the groove in them. That is usually caused by pad transfer or rust. Pad transfer occurs if you do hard braking or a lot of driving where you use the brakes and then stop and hold the brakes, the pads will heat up and transfer a microscopic layer of the resin in them to the rotor. Now you have patches of smooth iron and spots of resin that are different in friction. So, the brakes will slip, grab, slip, grab and that causes shake. To cure it you either replace the rotors or use a brake lathe to cut the surface to eliminate the surfaces. Then you have rotor damage, you are driving and use the brakes and then hit a water puddle. The water instantly cools areas on the rotors it hits. That can cause localized warpage, that can also cause shaking.

Thank you for your answer. what type of brake pads are required by Toyota . semi metallic or ceramic?

Factory pads are ceramic on that car. Front pads are 0446502070
Rear pads are 0446620090
Or an aftermarket equivalent.