the car takes roughly 4.5 liters of oil to fill, i typically put in about 5 liters with the filter and i use full synthetic and my car runs great, this is my second cobalt. hope this helps, you could also look in your owners manual, different year could use different amount.
sounds like a blown head gasket. Check for water in the oil. Excessive smoke coming out the tailpipe while idling. Smoke would be real white. You may need the head reworked