Engin oil in transmission?
Well if it is a Yanmar engine I find it pretty hard to believe that engine oil is leaking into the transmission. I know of no engine except some motorcycle engine/transmissions that has the ability to leak into the transmission as the flywheel is on the "outside" of the engine and the transmission connects to the "even more outside" side of the flywheel. The engine oil is kept inside the engine by a shaft seal that is on the engine side of the flywheel. To leak engine oil into the transmission the oil would have to make it past the engine shaft seal, down the crankcase rear end, up the transmission front end and through the transmission front shaft seal. Impossible!Other (non standard) transmission oiling meansDoes the transmission have an oil line from the engine? I've never seen this but I've not seen everything either.Coffee with cream is water in the oil and churned by the gears. This is bad! Does the transmission have a cooling system (most don't)? If yes this is most likely the source of the water. If no then the only thing I can think of is the transmission has a breather (I did not see one in the picture. It would look like a fitting on the top somewhere) and the transmission has been under water where the breather did its job and let the outside get inside. As for no forward gear, just overfilling the transmission will not cause the gear to not operate. It could be that gear selector ring has one side of its' bearing surface gone or the gears could be stripped. Either is going to require a tear down to inspect it repair it. The hard part of the tear down is getting the transmission out of and back into the boat. The actual transmission is simplicity itself and well with in the abilities of anybody who can change the oil on their car.What noises does the transmission make in reverse, neutral, and forward? How does the shift linkage "feel" when you are shifting it, soft, hard, clunky, grinding? These are the things inquiring mind want to know.Sorry I don't have better news but at least it is free.