When the engine cools down it should suck the fluid back into the radiator from the overflow bottle. If this doesn't happen then he's got a leak in his system somewhere.
The overflow bottle normally has a level mark on it and it should only be filled to that level when the engine is cold, otherwise if it's too full then it will overflow the overflow bottle.
Gearbox.... check the oil level and check the oil. If it's shitty and stinks then drain and refill the gearbox with clean oil.