poor installation most likely
The only time I've seen cracked spark plugs was putting them in or taking them out with the socket not perfectly straight.
Spark plugs don't smoke. A bad alternator would cause a dead battery.
Internal engine damage.
That strongly implies that the plug or plugs are not firing at all.
Worn spark plugs would cause mis-firing or non firing cylinders, both are no good for the engine, replacing the plugs may stop the knock (Could also be a different problem) But you should replace spark plugs as soon as possible.
start with dist cap and rotor
No, not unless your connect the plug wires wrong or one of the new spark plugs was bad.
Bad coil, rotor, distributor cap?
To answer this question it would be helpful to have more information for example if your vehicle is older with high miles a worn out distributer can cause this problem
the engine is constantly vibrating and it dislodges the spark plugs
bad fuel bad spark plugs incorrect timing
no gas entering piston chambers or no spark in the spark plugs. I assume the starter is spinning the engine?