[Three_Fingers]

A/C activation will turn on the fan even if the A/C system is empty-it's what it does.
Suspect a bad coolant temp sensor not turning the fan on when it should.
Dragging brakes is another matter...nothing to do with the engine.
Shaking engine can be caused by an ignition problem, a timing problem, a valve timing problem, an injector problem, or a blown head gasket/cracked head-all of which will cause misfires/rough running.
What engine ya got?