Low compression

Sounds like the piston rings are bad. That would account for all of the problems. Probably would be a good candidate for a good used engine or a new long block and use the current engine as a core. If there is nothing else wrong with the car.

Did a compression test on each cylinder.
the minimum is 199 psi cylinder

1:100
2:120
3:125
4:100

When i first start the car it seems to shake, sputter. after the 2nd or 3rd start it fires up runs rough than smooths out.

The only code that is showing is cylinder 2 misfire, pulled plug.
plug is normal, checked all all were good

The 2.2 Mazda doe's not have a valve adjustment and the smoking is from the head. The head has a valley where oil is kept at all times and the valve train is there as well valve guide seals will crack and oil will go into the cylinders. This is where you get the smoke from and some time they will not stop smoking notice on the exhaust manifold there are four caps take the caps off and you will see the cylinder that is wasting the oil valve guide crack are brake and this motor will smoke up the town. The valve train is under the oil line and that is why it will smoke notice when you pull the head there is a restricker there with the head gasket it is about the size of a dime be sure you put a new one back in it will come with the head set. If you don't put it back in it will put all the oil into the head and empty the oil pan these are very well built motors.

It sounds like the engine needs a valve job, I would pull the head and check the intake and exhaust valve for leakage.