Getting electrical ignition parts wet will cause a misfire that will continue until the water is dried out or evaporates.
Yes, it is possible.
check motor mounts
check the motor mounts
The exhaust might shake, not the motor I had dual side exhaust on my 88 350 ran sweet!
Loose Motor Mounts
not usually. warped rotors will cause a vibration during braking.
It might be a broken motor mount or transmission mount.
If your car shakes while accelerating check your motor mounts. Then check your transmission.
Shake them hard or wash them.
Shake the vechicle
Possibly a bad motor mount
A failed cv shaft or a broken motor mount are most likely.