In order of least expensive repairs
1 blown Head gasket
2 cracked head
3 cracked block
If water is coming from the exhaust check your oil if it is going white water is mixing with it stop the motor before you wreck the bearings.
I feel these are unrelated but you can investigate a leak in the hoses leading to the heater core as they maybe leaking onto the exhaust pipe, that would produce white smoke, but not from within the tailpipe exhaust. Water and oil leaks will produce white smoke the smell will help you determine which it is.
White smoke means water, blue/black smoke means oil, black smoke can also mean the fuel mixture is too rich.
Engine exhaust turns white from water in the combustion chamber.
it would cause overheating but the smoke is probally coming from some sort of water or antifreeze in combustion chamber
The smell of rotten egg is coming from your catalytic converter that is plugged up White smoke is an indication of water (usually antifreeze) in the exhaust.
White smoke especially when starting tends to indicate that water is finding its way into the the exhaust system, where it is boiling and exiting the exhaust as steam. The possible cause could be water getting into the cylinders (perhaps from a damaged gasket).
White smoke is water vapor (or coolant) in the exhaust, the black smoke is the (normal) over-rich condition at WOT (full acceleration) White smoke can also be unburned fuel, generally seen on earlier, non-electronic engines that are mistimed.
Dont filled oil so that no smoke
White smoke from the exhaust indicates that your car is burning water in the combustion chamber. This is an indication of a bad head gasket.
valve seal
Moisture in the exhaust, or a cold running engine.
Coolant getting into the fuel or oil.