The high-speed vibration when braking at high speed is usually the front brake rotors are warped which can make the traction control light come on.
Here is how to replace the front rotors and pads which sound like they are worn out. You can get the parts from Amazon. Also, please start a new question for your other problems because they won't have anything to do with the brake problem. Please check out this guide:
https://www.2carpros.com/articles/steering-wheel-shakes-when-accelerating-or-braking
Check out the images (below). Let us know what happens and please upload pictures or videos of the problem so we can see what's going on.
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Tuesday, October 3rd, 2023 AT 12:10 PM