Brake pedal sticking

My 2000 F-250 is having problems with the brakes. When I coast, it’s like the brakes are on. While parked, I noticed the brake lights on, and manually lifted the pedal to make them go off.

I’m also getting a shake when I’m driving over 45mph, don’t know if it’s related.

Not related. A mechanic needs to determine if there is a weak spring, or other cause for the gas pedal not returning. He could also check out that shake.

Brake pedal, not gas.

The brake switch may be out of adjustment. It is located under the dash, and is actuated by a plate on the brake pedal lever.

You could have dragging brakes. Or bad wheel bearings also make it seem like that. Bad wheel bearings could also explain the shaking. Get this checked out immediately.