Look at the car if you can
There are a lot of folks out there selling cars on the net, Ebay especially and asking a lot of questions and even seeing the car is a real plus. To answer your questions without seeing the car or being able to inquire to the seller further I'll take a stab at it. The low idle when engine is cold could be a number of things that could either need adjustment or replacement. Just how cold is the outside air that the seller is talking about? Here's a few things that could directly affect idle on a cold engine. Idle set to low to start with, look at tach to verify it's idling between 750-850 rpm, bad or going glow plugs would not only cause a rough starting idle but also causes a very hard to start engine, hence the battery replacement they could be talking about. Glow plugs are relatively cheap, $12 a piece, need to change all five at the same time just for piece of mind. Valve adjustment could be required, DIY'er with a new $7 valve cover gasket. Injection timing could be off, but in most cases it affects the engine in cold or hot engine running conditions.
The sunroof needs a fuse, I don't buy that one. Why mention that it just needs a fuse when a $.09 fuse installed would cure the problem? I'd say that either the sunroof motor is toast blowing the fuse, the clutch is either out of adjustment or broken or the cable is snapped and also requires replacement, (That one isn't real fun to do, but is also a DIY'er project if you have patience) Roof motor new runs over $300. or at salvage yard about $75 The cable runs about $42 and only buy this new.
The rust on wheel I assume is meant to mean that there is rust formation on the rear wheel fender lip, pretty common if this is a Northern car. It to can most likely be repaired or at least slowed down from growing.
Not much else was mentioned in your post about how the seller rated the engine performance or tranny shifts. I'd like to know as a buyer how the engine has been maintain as well as the tranny as either one that has been abused can cause headaches and empty wallet syndrome down the road.
Mileage on this car is still quite reasonable and you would probably be able to double this if the engine has been properly maintained. I think I would start asking in dept questions about every feature of this car from seats to climate control for proper operation. I'd keep these emails as well and somewhere get in writing that if it is not as described seller must refund you your money.
You'll probably find that a lot of folks that are selling their Benz on the net either take it in to a shop for all repairs, thus a less detailed description of how the car looks or performs verses the person that maintains their own car that lists replacement parts recently changed or repairs that have been performed. These DIY'ers generally have a heads up on how the car performs and whether it has degraded or not.
"Tell me and I will listen, Teach me and I will learn, Show me and I will accomplish, Involve me and I will succeed."
'84 300SD 256,000 Gold on Brown (Mileage Award)
'86 300E 246,000 Blue on Tan