Cylinder 6 is the rear driver's side cylinder(LHD) and the lower intake has a coolant passage right next to the runner (just pass through to cylinder head, intake isn't cooled) so if the gasket is bad, or manifold is not properly tightened, you may be leaking coolant out as well as allowing some into the intake runner for cylinder 6, which could be causing every problem you described.
Replace the gasket. If you are burning coolant, best case would be destroying your catalytic converter in the near future, worst case would be hydrolocking the motor completely.
As to the water in the oil cap, I would get an oil change, and monitor it. Some condensation is normal, more if you drive more short trips then long, but could also potentially be a sign of a serious issue.