You can check it when the engine is cold and you should check the oil level in your engine when the engine has sat for at least 30 minutes. This way all the oil has drained back into the oil pan and you will get an accurate reading on the dipstick.
Cold
Check the oil pump housing gasket
Check engine oil when you have just finished driving. Check Transmission fluid when the car is running and the transmission in in N (manual) or P (automatic).
Makes no difference if the engine is warm or cold. Just make sure the engine has not been run for at least 30 minutes before checking the oil level. This way you will get a very accurate reading. I normally check my oil level after the car has sat overnight.
With engine cold (prior to first starting in the morning) and parked on level ground - remove dipstick and check oil level as shown
No, oil level does not cause the check engine light.
Only in an emergency. The computer will turn on the check engine light if the temp never reaches normal. A cold running engine is also more prone to oil sludge problems.Only in an emergency. The computer will turn on the check engine light if the temp never reaches normal. A cold running engine is also more prone to oil sludge problems.
To change the oil depends on the engine model. Check your engine model first in the registration and go to the technical information in your BMW z3 booklet. To compensate the leaks or oil consumption (oil burned in the engine) you have to check the level on the dipstick. The oil level in the engine (cold) should be between the two signs on the dipstick. Never over fill and use the same quality of oil.
Overheating ? - Check radiator for water and coolant, and engine for enough oil and not old burnt oil
Valve clatter? Check oil level and pressure? Fuel mixture?
On the dipstick there is a safe range. You can check it either hot or cold. When cold the level should be close to the bottom of the safe range. When hot it should be close to the top of the safe range.
The check engine light does not generally have anything to do with the check oil light. The oil light just indicated it is time to change the oil, while the engine light indicates a problem.