Not likely but it is possible.
A dead battery would not cause an engine to seize
It would if the battery voltage was lowered enough to cause it not to fire.
Well, theoretically, if the neutron of your management crisis went into flames, you would blame your engine propeller and fan. Your engine management unit only catches fire if not cooled down regularly.
a weak battery will not cause an engine vibration.
Weak battery? Loose or corroded battery cables? Starter solenoid?
Could be, (assuming the starter is not cranking the engine) a bad starter, dirty or loose battery connections, the engine is seized.
Engine speed sensor faulty. Dead battery or batteries. Loose or dirty battery connection. Dead spot on starter.
If the alternator fails, it is no longer keeping the battery charged and your engine is running on nothing but battery power. Once the battery runs down, your engine will no longer run.
Dead battery, seized engine, lack of air or gas,
Possibly. Under some circumstances it could cause the battery to short out. If the engine has been running hot for long periods, the heat could damage the battery too. It might also be that the engine has internal damage and the starter is having a problem turning it over.
The alternator produces power to charge the battery. The battery powers the starter to turn the engine over.
yes if one of the wires was getting an earth from the alternator cover or rubbing off the engine the battery light is really an alternator light warning you that the alternator is not charging the battery