Vehicle vibrates after being driven for a while

Hello, I just bought this car and have noticed a vehicle vibration after it is warmed up. It seems to be much worse if it is hot outside and has been driven for a little while. The vibration is in the floorboard at lower speeds, and in the steering wheel at higher speeds. Almost like an out of balance tire, but it does not always do it. It is hardly noticeable in the mornings when it is cool outside. Occasionally I have noticed it feels like the rear brakes are being applied when I am accelerating up a hill (you can feel hesitation and a little hop in the rear). Also, when the car has been driven for a while, I feel some jump/thump in the floorboard when braking. I attached pictures of left and right rear rotors. Looks like some deposits, but not sure this would cause all my issues.

FYI- I have two brand new Michelin tires on the front and two original on the rear. The rear tires do show some cupping and have been on the rear since 15,000 miles (the Lexus dealership has the previous owners records and when I bought the vehicle from them, I did not notice they skimped on putting all four new tires on. Now they refuse to do so).