No, low coolant would cause the opposite.
If you have coolant on the top of the engine it could be a leaky thermostat housing or a leaking intake gasket.
A leaking heater core will cause the engine to overheat because the coolant is leaking out.
head gasket is leaking into oil
heater core leaking
It could just be condensation which forms in the exhaust system outside of the engine, or you could be leaking coolant into your engine (typically via the head or intake manifold gasket).
If your heater core is LEAKING engine coolant so that your engine coolant level drops too low or the engine coolant is lost completely and causes your engine to overheat then your engine can be damaged beside the mess the leaking coolant makes inside your vehicle ( you might be able to just temporarily bypass the heater core so that no engine coolant is flowing through the heater core )
If by water you mean engine coolant, yes. Loss of coolant, antifreeze, is a major cause of overheating.
Intake manifold gasket
This sounds like bad news. The coolant could be leaking into your engine and mixing with the engine oil, then cooking off. A simple test can tell if there's water in your oil.
I think you may be referring to coolant leaking from engine? engine coolant or water can leak from any coolant hose or heater hose, waterpump, thermostat housing etc, wurse case the head gasket is leaking coolant externally, need a pro to check it out
No, only a blown head gasket or cracked head will cause coolant to mix with the oil. A leaking valve cover gasket will only cause oil to leak onto the engine block externally.
maybe catalytic coverter clogged, leaking coolant hoses to/from heater core, hopefully this helps.