Low oil pressure light and buzzer goes off when cold (below 20') engine starting.

If the oil level isn't going up, the coolant is more likely leaking through a cylinder head gasket. GM engines often have intake manifold gaskets leaking too. That would be much more common than a leaking head gasket on their truck engines.

Consider adding a small bottle of dark purple dye to the coolant, then search a few days later with a black light. The dye will show up as a bright yellow stain that you can follow back to the source. If you find it inside the tail pipe, suspect a leaking cylinder head gasket. You can find the dye at auto parts stores, and those that rent or borrow tools should have the black light. If you find traces of dye in the oil, the head gaskets will be the likely suspects. There's coolant passages in the heads and oil drain-back holes. Leakage between these two is not real common.

For the oil pressure issue, any testing has to be done while the problem is occurring. We call the red Dex-Cool antifreeze "Dex-Mud". You'll get differing opinions on when it turns into sludge and with which other fluids. One of the most important things is to not listen to GM's recommendations. They falsely listed it as "lifetime" antifreeze to make their cost of maintenance appear to be lower than that of their competitors, but then on the reservoir there's a sticker that says to replace it every three years. Antifreeze will always be antifreeze. It's the water pump lubricant and corrosion inhibitor additives that wear out in about two years. Failing to replace the coolant every two years is one of the big reasons GM has so much trouble with leaking heater cores and radiators. You can test for the normal acid buildup in the coolant with a digital voltmeter. Place one probe on the battery's negative post and touch the other one in the coolant in the radiator, (but don't touch it to anything metal). If you find anything over about two volts, replace the coolant.