As far as the rumbling in the cabin that could be an indicator that your motor mounts are needing to be replaced. How many miles on the car? Does it feel like the engine is missing? Sounds like your idle is uneven. When was the car last serviced and tuned ie. plugs, filters, wires etc.? Have you checked to see if the car has recorded any fault codes? Do you know if the engine wiring harness has been replaced?