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Yes
Yes, fouled spark plugs can cause engine shaking, and loss or power. I'm not sure about knocking but I'd guess that too.
If an engine was not assembled properly it could cause a low power complaint.If an engine was not assembled properly it could cause a low power complaint.
Probably not. A plugged cat would cause a loss of power and the check engine light may come on depending on what year and model vehicle you have.
Yes, it is possible. It will also cause severe loss of power.
Loss of power when accelerating can be caused by a number of things. A leak in the fuel line or even a bad alternator can cause this.
If the cat was damaged and restricting the exhaust it could cause a random misfire (P0300) but you would also have a severe loss of power.
Your piston rings are probably bad. Which will cause compression loss, in effect you will loss power, and it will let oil trough and saturate your plugs.
dead battery
A plugged fuel filter, A plugged catalytic converter,
I would start with your battery.
The first thing that comes to mind is the catalytic converter plugging up after driving a short distance and clearing itself after sitting for a period of time. Take it to a muffler shop for an expert opinion. The plugging of the converter would cause a huge power loss and the resulting restricted exhaust gasses would cause your check engine light to come on since the oxygen sensor would be giving the computer bad information.