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First make sure the valve covers seals are not leaking. 2003 its about that time the valve covers will start leaking oil. Under load ie going up a hill this would match your description.
Coolant you need to pop the cap off when the car is cool and make sure it has coolant in the radiator.
HG issues more often than not are tied to a few things with cars beyond the 2002 gasket design problem. If your car sat parked for long periods of time and you have a very spotty oil change history that will actually cause gasket issues. This would fit the valve cover gasket leak ie oil problem you describe and could contribute to a failed HG involving coolant loss. Just about any brand car will have similar issues when the oil is not maintained and the car is stored for a long period of time etc.
Coolant you need to pop the cap off when the car is cool and make sure it has coolant in the radiator.
HG issues more often than not are tied to a few things with cars beyond the 2002 gasket design problem. If your car sat parked for long periods of time and you have a very spotty oil change history that will actually cause gasket issues. This would fit the valve cover gasket leak ie oil problem you describe and could contribute to a failed HG involving coolant loss. Just about any brand car will have similar issues when the oil is not maintained and the car is stored for a long period of time etc.