Sorry for the double post, I took too long to edit my original post and it wouldn't let me edit and repost.
To the OP,
All BMW automatic transmissions have now been retroactively approved to use DEXRON VI. Prior to that, the specs were byzantine. Thankfully, now just use Dex VI. Breaking with tradition, the genuine fluid from the dealer is now reasonably priced, but I checked with one of the few approved ZF transmission re-builders in the US and he said he would not hesitate to use Maxlife. It's inexpensive at Walmart. In fact, I drain and fill at 30K and drain fill and change the filter at 60K. He strongly recommended the BMW filter or Filtran brand ONLY (don't know if the GM tranny uses a Filtran filter). I live in the desert, so its a severe service situation. Anyway, he is a re-builder and should know, says stick to those filters.
I use Maxlife in a 740i (261K), X3 (135K) and a E46 325i (167K) with good results. I went conservative on the transmission filters as some folks have had problems with non-OE filters. The refill procedure is VERY important, lots online at e90post, e46fanatics or bimmerfest on this topic. Your GM transmission is made in Stausburg France, and is very different than stateside GM transmissions. Remember, all the chatter about which fluid to use is now obsolete with the change of spec to Dex VI.
BMW has backed off lifetime fill and now recommends 100K miles. ZF recommends 60K. I know yours is GM, but don't hesitate to change it.
Important: If you choose to use Maxlife, ONLY USE the one with all the German car approvals on the back label. There are a couple different flavors of Maxlife, ONLY use this one.
I am using Ravenol transfer case fluid for less than 1/2 the BMW part. There is chatter about the company on this board, I'm convinced it's good stuff. Available from Blauparts, distributor of Ravenol in North America. Change it at 60K, it's an expensive repair if it fails, and its a friggin' quart of oil, change it! SHAKE WELL before using, some good bits settle out to the bottom of the bottle.
Power steering at some point in time has changed from Dexron III ATF to CHF 11S. YOU REALLY DON'T WANT TO MIX THE TWO. Check the fill cap, it should say either of the two. The manual is a good source too, but in transition years, they can conflict. Use the cap as your guide. My personal experience with several cars is the PS starts to moan a bit at about 60K, flushing the fluid fixes the noise. I use the Ghetto method: turkey baster and drain and refill from the reservoir, drive for a few minutes turning full lock right and left, repeat two more times and use a full liter. Some cars don't experience the moan, but one of the four hoses in the system typically leak before 60K and gets changed and the system refilled, so they've effectively had a fluid change. You decide. Use squeaky clean baster, containers and funnels; these systems don't like any dirt at all. Tip: there is a very small hole in the cap to breath, clean it well and you wont get the constant weeping of fluid around the cap. If it's ATF, I use Redline D4 ATF, if CHF 11S, I use Fuchs. Don't over or under fill this system. Most don't know, but the reservoir itself has a filter at the bottom, I change it at the second (120K) interval or sooner OR if there is any evidence of any debris in the fluid. One of my cars had [censored] in it at 60K. Use OE suppliers such as ZF, ATE or Conteco.
You have self leveling suspension? This I believe has always been CHF 11S. I like FUCHS, big lubricant producer with a very good reputation and the price is right compared to Pentosin. I found the best deal at Pelican Parts.
If I am in error on my lube specs or recommended procedures here, somebody please chime in and correct me. I have no interest in any of the brands or vendors mentioned here, just owned and tracked and worked on a bunch of Bimmers over the past 25 years.
My 1st post on this board, hope that helps!