Hi and welcome to the forum.
My E39 had a seperate transmission oil cooler, and looking http://www.realoem.com/bmw/showparts.do?model=DE22&mospid=47547&btnr=17_0106&hg=17&fg=05" rel="nofollow - here it would appear you too have a separate transmission oil cooler. You should have a cooler for power steering, one for engine oil, one for engine coolant, one for transmission oil and one for the aircon.
Any decent car with an autobox should have a transmission cooler to cool the oil, this prevents damage to the internal oily parts of the gearbox when it is under load, i.e. when you are towing or giving it plenty right foot.
Engine coolant radiators on Mercs and Vauxhalls(GM) use a combined unit for engine coolant and tranmsission oil colling. This method uses engine coolant to cool tranmsission oil, not engine coolant to heat transmission oil. The transmission will hold lower gears for longer to a) heat the tranmsission up quicker and b) to heat the engine cats up to operating temperature. It was a common fault on Mercs for the transmission oil cooler to leak into the engine coolant radiator and cause failure of the autobox aas it was now being lubricated by coolant which obviously is not good for any moving components. More often than not the transmission was a right off and they needed a new radiator as it is a combined unit. Reading your post I thought this would have happened to your car from the faults you describe with your autobox, but I'm failry sure you have seperate cooling units as I mentioned above thus eliminating this type of failure.
I would say you have two problems, your transmission is in need of a service to look at the rough shifts and the second problem I would suggest is a blown cylinder head gasket which is allowing oil and water to mix. Look under your oil filler cap, if a white substance is present there then this would confirm the cylinder head gasket failure.
The E39 is one of many BMWS inflicted with a sealed for life transmission thus there is no way for a diyer to check the fluid level so any problems really need taken to a transmission specialist to be diagnosed. Saying that the ZF boxes fitted to these cars is fairly bomb proof. It could just be low fluid level.
Have a look under the oil filler cap for a starter and let us know.
Andrew
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