Well something is adding to the volume of your oil unless maybe it's just foamy, and making it that brown color, like was mentioned, coolant usually looks different and you are not loosing or gaining coolant, and there is no oil in the coolant so that makes a cooler problem unlikely. If the pickup tube for the trans filter is damaged and sucking air it would explain needing needing to rev the engine in order to engage the transmission and maybe explain the foamed oil and the clutch packs have been damaged/burnt which might explain the colour but does it smell?? If the transmission vent, which is supposed to be open to atmosphere, is maybe hooked into the CCCV system somehow it might explain some of the increased volume and colour of the trans oil. Too high an oil level in the trans can cause foaming as well so there could be a variety of things going on. Like was said, it's easy to get fooled by pictures so maybe take a sample of the oil, or better, the vehicle to transmission shop and see what they say.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)