I too have an 88 560sel. it also is my baby. I have had it for 3 years and have already socked over $15,000CDN in repairs into it. But it is worth it. I had the whole car stripped down and all rust removed and new metal put in and then had the car reassembled and repainted and hand polished to a mirror shine. I replaced the front windshield and rear window and redid the burl wood trim inside the car. The car looks mint and I cannot get a new car with all the features this one has for what this one cost me. I am still about $2,000 away from saying it is perfect. But enough about me. Any older car will need maintenace on a regular basis. The trick is to get all the bugs out first - then just maintain it.
My car had a mysterious white puff of smoke with the smell of burnt oil on the passenger side of the engine every now and then. After trying to find it for over a year and 3 valve cover gaskets later - the Mercedes dealer up here just told me the valve cover was warped in the rear. Why did your mechanic tell you to change yours? I am going to take Mercede's advice and send my cover to a machine shop and have the bottom sealing edge machined flat at a cost of $40-75 CDN. If yours is the same problem - maybe you can save some money this way.
As for the shaky idle - been there - go to tech help search and type in "idle control valve" Check the procedure to clean it - should solve your problem - Also suggest you pour a couple of cans of injector cleaner or that more expensive fuel system conditioner cleaner (I use the stuff by Duralube) into your gas tank - you may have dirty injectors causing the shake. Worst case - look up thread from me on rusty fuel line replacement - it will explain that problem to you and what Henry did to cure his recurring rough idle as a cheap fix.
As for the self leveling container - clean the outside of the case real good and you should be able to see the fluid level in it. It should be at least 2/3 full. If I remember right there is a level mark on the case - but don't remember - as long as mine is over the ridge around the container above the spring holding it by about 1" I call it full. Search for threads on car not being level with hydraulic suspension - loads of info available. Use recommended Mercedes hydraulic fluid when you top up - not anything else.
With your ABS light on - search for threads on OVP relay - Also note - if you ever have your car jump started and it doe not run right after the jump start - the fuse on the OVP will be blown.
Aux fans - been there - note: when the engine temp reaches 107C the aux fan will come on high and not shut off until temp goes down under 100C. When you get your air conditioner fixed - there is another aux fan sensor near the drier that will kick the aux fan on low when the pressure in the air conditioner gets to a certain value. Unless either of the two abve scenarios are achieved - that fan will not go on. learned that the hard way!!
Outside temp - if the only acts up in the car wash - check the leads to the sensor - they may be corroded. Other than that - don't know - mine always has worked.
As you get deeper into this car - go to search and read all the posts by Mike Tangas - he descibes all the problems he had refurbishing his 560 and gives detailed instructions on how to do the repairs he did.
I saved the worst to last - Timing chain and guides and tensioner.
Definately read Mike's post on this subject and he describes how to do it yourself. If your car has over 150,000 miles on it - it is time. To check the condition of your plastic guides to see if they are still good or not - remove the passenger side valve cover and look at the long guide on the timing chain going to the cam. If it is white - it is new - if it is amber - it is OK - if it is brown like the color of a beer bottle - DANGER - replace immediately- they crack and the timing belt comes loose and $$$$$$$$$$. The upper guides and tensioner are cheap - With Mike's guidance from his posts - it is a DIY job.
All the best and good luck!!