When applying the brakes the brake pedal and steering wheel shakes

The rotors look okay, but it's very hard to tell from a picture. For the price of new ones and as you have those off already I would clean the hub surface of any rust and put new ones on. However the issue could be two fold with the rear brakes causing the shaking pedal and a front tire out of balance causing the steering wheel shake.
First thing would be change the rotors, if the issue is gone then it is likely that those rotors are either bent "warped" or they have thickness variations. If the problem is still there rotate the tires and see what that does. If it's still there then you will want to look at the suspension for loose parts like ball joints or tie rod ends.

Thank you for the reply. I purchased the car July 2018. It has been going on since. It never bothered me. So i never did anything about it. The steering wheel and entire car vibrated at high speeds. That was due to bad rims and tires. I changed both. Kind of solved the issue. They were balanced and all and still continued. A few weeks ago. I removed all wheels and tires to clean them. And the vibration stopped at high speeds. (Do you know why) And that’s when the brake shaking bothered me as it’s what’s left to make it a smooth ride. So I believe the whole wheel situation is out of discussion. But also. Can the rotors cause shaking for such a long time without causing other issues. As there seems to not be any.

I would go over the tires as well. It's really easy to have one out of round or with some broken belts from a pothole or hard bump. It would still balance good but it will be like riding on square tires. If the tire removal made a big difference those are the first step. Then go over the brakes, they would cause a shake or pull if the rotors were warped or if they have thickness variations, then suspension items being loose. When you are driving all of those spinning parts from the axle, hub, rotor, wheel and tire create a lot of force. I have driven past cars with tires so out of balance they looked like a basketball being dribbled, but inside the car they didn't even notice the problem. Usually as you get to the center of the mass it creates less force so the biggest item is the tire, then the rim, then the rotor and finally the axle and hub, but if you have a bad wheel bearing the entire assembly will move and shake. An out of balance tire with a bad strut can make it feel like you're driving a paint shaker.

Thank you again. The shaking while driving at high speeds is gone. So like I said. The wheels and tires may be out of discussion. The only issue I have now is when braking. The axles were repaired not too long ago. Visually they look good. And like I said. No more shaking. Struts are definitely good. So now my plan is to replace the rotors. I really appreciate the help. Thank you.

Okay, if the only issue is while braking, swap the rotors, replace the pads and make sure the calipers are good and moving as they should. Might be a good idea to check the rears while you have it apart, just as a precaution.