What does it mean if there's oil in my radiator?
Means you have a leak between the oil system and the cooling system. Probably means you also have coolant antifreeze in your oil... check the dipstick for water contamination. That's a worse problem.This is bad and is a sign that the walls between the coolant and lubrication system have corroded through (from depleted coolant - too old) or your engine block is cracked from freezing or severe overheating. Both oil and coolant travel through passageways in the block and the walls between them can be thin. Another possibility is a head gasket failure.This is not a totally uncommon ocurrence I have heard, and to fix Head gasket is not too bad but the corrosion or cracked block will likely be expensive. Continuing to drive this way will eventually destroy the engine totally (it's not that far from there now, even though it may be running). The watery oil will foam and be ineffective. the metal parts will rust and eventually the engine will seize as the hole gets bigger and the leak worse.
What does it mean when my coolant light comes on for just a few minutes, and then goes away once I start driving?
Engine coolant has a variable volume that changes with temperature. When cold, it takes up less space and could therefore be below the coolant level sensor (if equipped). Upon reaching a higher temperature as the engine warms up, the coolant expands and makes up the volume to flood the sensor.The test (and remedy) is to check the coolant level and fill to the minimum line on the reservoir. If the light no longer comes on when starting, monitor the level to determine if coolant is leaking or being consumed through a failed head gasket. This is often evident by white smoke from the tailpipe and an antifreeze odor in the exhaust.