Vibrate at idle after hitting curb
Have someone check the motor mounts. Some Mazda 3’s had weak ones.
You broke the car. Take it to a shop that can repair all the damage.
Although this isn’t your issue, you should also have the suspension inspected for damage that could be unsafe.
There, I fixed it for you!
Note to the OP:
Damage to suspension/steering components and other parts in the front end may not be immediately apparent, but they can still present significant safety hazards. An impact that was strong enough to damage the motor mounts is definitely strong enough to bend a wheel and/or a suspension arm, and to damage wheel bearings.