Rough Idle on Mazda 3 2006 Hatchback

My Question: Is it the Passenger Motor Mount, the throttle, the EPA
Solvenoid, the Rear Motor Mount or something else?

Last week I took a rough slide on some dirt road and then the bottom of my
car started vibrating rough. Consequently, when driving, the gas pedal would
create a noise sort of like a chainsaw, it sounded like I had a "turbo exhaust".
Fast-forward to three days after that, I installed a K&N Typhoon 69 Cold Air
Intake and now.. I cannot hear the earlier stated noise.

Here is another brief description of the issue: Car has a very aggressive
vibration in the cabin on the steering wheel at times, the seats and near the
passenger seat/glove compartment. I checked my PMM earlier and it looks
identical to the recently OEM purchased OEM Mazda PMM. I have not yet
checked the RMM, but, when the car started vibrating last week, I
instinctively went to check the bottom of the middle of the car.

This car has 191,000 mi. I purchased her at 133,000. No recent incidents. A
2006 Mazda-3S Hatchback with Auto Trans.