No, but you can cause excess wear on the engine. Oil gets dirty and that dirt will cause engine wear and sludge. Change the oil & filter every 5,000 miles or as outlined in your owners manual. Engines are very expensive, but oil is not near as expensive.
Eventually the engine will seize.
This is usually accomplished by either forgetting to refil the crankcase after an oil change, or by running the engine out of oil by not routinely checking the oil level, and adding the appropriate amount when it's running low. It is also possible to seize an engine by overheating it.
Probably not, but its a practice to be avoided
The engine could possibly seize.
The engine will overheat and the pistons will seize.
No, it would cause the engine to run poorly but not to seize. Lack of lubrication or overheating will cause that. Also a broken part, as in a rod, will cause it to seize.
A dead battery would not cause an engine to seize
Eventually one of two things will happen. 1. The oil will sludge up and clog up the engine, then all the critical components won't receive oil and the engine will seize. 2. The engine will use all the oil, then all the critical components won't receive oil and the engine will seize. In the end, bad things will happen regardless
you do not check the oil in the engine and the engine gets too hot
Run it out of oil.
Sugar
It could if the valves made contact with the pistons in an interference engine.