Depends on what's fouling them. If the plug is wet with gasoline, it's because there's no spark there to burn it off. Solution could be as simple as replacing the plugs and gapping them correctly. If it's fouled with a nasty oily sludge you've got oil seeping past your piston rings into the combustion chamber, which means either your rings or bores or both are pretty shot.
Spark plugs don't smoke. A bad alternator would cause a dead battery.
That strongly implies that the plug or plugs are not firing at all.
Internal engine damage.
poor installation most likely
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.
The only time I've seen cracked spark plugs was putting them in or taking them out with the socket not perfectly straight.
Bad coil, rotor, distributor cap?
my 1993 probe gt done the same thing with the no spark at the plugs the ignition module was bad i replace the whole distributor and it runs great
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