Is this reply for real???
If there is oil on the coolant, the head gasket COULD have failed, but you could also have a leak from the coolant pump gasket into the oil, but the fact that the engine is down on power as well COULD be an indication of this type of problem.
Whenever you find that the oil is low or that the engine 'rattles' (due to low oil level) stop the engine IMMEDIATELY as continued running can ruin it within seconds.
The 'mayonnaise' that you get on the inside of the oil filler cap is normally due to condensation and can be worse if the car is used only for short journeys, particularly in cold weather.
If the engine is in good condition, there should be NO migration of oil into coolant or coolant into oil.
There is more to diagnosing a failed HG than looking for 'mayo' in the oil cap. There have been many engines needlessly stripped down because people (professional and otherwise) have misdiagnosed the problem.
Symptoms COULD include: Misfire, Oil in coolant', Coolant in oil, 'Mayo' in oil filler cap, Water from the exhaust (again, this could be condensation), Low compression on one or more cylinders. Lack of power, In extreme conditions, the engine may fail to turn on the starter, due to coolant in a cylinder.
Both petrol and Diesel engines have a pressure relief valve in the cooling system, which should relieve any excess pressure to atmosphere.
Your gear selection problem probably is not related and may well be down to the linkage being slightly out of adjustment.