FWIW - the original fluid is not red. Sort of dark gray to brown. Hard to know what is in there other than its red. A couple of fill and drain cycles may help with some fresh & known fluid. The cooler and torque converter holds ~3 quarts. You usually get ~6 quarts out when you drain it and drop the pan. (roughly 2/3 total fluid). Repeat twice and you are up to 8/9. The third time gets you to 26/27... I use Pentosin ATF1. 5-liter jugs are available for $50 or so. Be suspicious of shops offering to flush the transmission for you. It is unlikely they are throwing away 15 to 20 liters of good synthetic fluid in the flush (especially if they haven't priced in $200-$400 for fluid). Most likely to be some generic stuff unrelated to the ZF/BMW spec.

The selector switch (that crushed wire) is known to go bad over time. I wouldn't work too hard trying to fix an old one. The switch comes as an assembly and includes the hard plastic sleeve and the circular plastic connector you mentioned was loose.

The temperature sensor is an easy repair once you have the pan off - cheaper even than that selector switch.

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David.X5
2001 X5 4.4i Sport
SOLD! at 160k miles