Oil light

If the engine stopped first, then the oil light turned on, that is normal. The engine drives the oil pump, and the pump develops the oil pressure. The pump does not run when the engine is stopped.

"Some" oil in the engine can lead to a major engine failure. The level needs to be at least up to the "Min" mark on the dip stick after the engine has been off for a few minutes. Remove the dip stick, wipe it off to remove the oil that splashed up higher, then use it to check the level.