I would suggest you buy the ATSG book for this transmission, It will tell you a lot of how to adjust end play of the output shaft with shims and how to test clutch pack play with a dial gauge.

It is a pretty good book. well worth the 30 dollars.

regarding the cooler lines, the driver side one is the supply to the cooler.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)