How to remove head gasket on 1997 jimmy

Causes include, cracked block, cracked liner, warped head, incorrect gasket used (non OEM) etc etc etc.
Remove the plugs/injectors and during a coolant pressure check, look for spray inside the cylinders.

Oil mixing with water is mainly due to head gasket that has blown between ports.

Transmission cooler inside the plastic parts of the radiator may be leaking and causing the oil to mix with the coolant. GM also has a problem with their lower intake gaskets leaking, which would allow the oil and coolant to mix. Last possibility is the head gasket is leaking and mixing the oil into the coolant side but not the other way. Check your transmission fluid for mixing evidence. Another thing to do is pressure test your cooling system (Radiator, hoses ect) to see if there is a leak. Another test to try out is compression.

The only place, oil and water share a gasket is the cylinder head gasket, oil and water galleries run through the engine block and head via the head gasket. The cylinder pressure will be OK, it's the oil pressure that's putting the oil in the coolant, the gasket has gone between the water and oil galleries or there is an internal crack (unlikely). A coolant pressure test should show it up.

From what you are describing, I would say that the head gasket could be the cause. You have water and oil passages that run through the heads. If the gaskets have deteriorated, it will allow the oil and water to mix.

Oil and coolant mixed usually means the engine is damaged.
Blown head gasket, or cracked block - head.
You may have coolant in the engine oil too.
I would not drive it.

Faulty blower motor resistor

you more than likely have a blown head gasket ...

Water in oil usually means that is time for replacing the head gasket.

See: - HOW TO TEST FOR A FAILED HEAD GASKET

This sounds like a blown cylinder had gasket. Although on some engines you will find core plugs below the rocker coverin the head.