Yes.
Yes, bad spark pugs or plug wires can cause the engine cylinder to misfire which will cause the engine to vibrate.
Yes.
as a result of bad spark plugs
Contaminated fuel could cause a misfire.
yes
the motor mount is bad
Yes.
yes
Yes.
Yes they could be cleaned and battery charged
Yes. Totally! If the engine mounts are bad the whole car will vibrate and run bad. Get it fixed.
Yes, either can cause a shake while driving.