OK, to address some of the minor stuff first. Your missing hose runs from the Fuel Pressure Regulator to the air filter housing breather hose,
afaik it is only there to siphon off fuel if the FPR diapraghm springs a leak.
Your OPV should not rattle. If you open it up you will see a relay, which can get stuck. A malfunction in this unit affects current flow to the Idle Control Valve, which i assume is what you refer to as the IAC. There are also some soldered connections inside which crack and can cause problems. If you have antilock brakes, a faulty OPV will cause the ABS light to come on as it runs on the same circuit.
Disconnecting the power from the ICV while the engine is running will affect the idle as with no power the unit reverts to limp home mode, which iirc fixes the idle at around 600 rpm, less than normal, which is enough to get you home without idle control but you will find the motor has a tendency to stall.
Test the OPV by disconnecting the lead from the ICV and measure the voltage between the sockets while the engine is running. If the OPV is OK, there should be around 6v. If it fluctuates, or drops to zero, chances are the OPV is bad, Worst case scenario your engine control unit is shot. Mine was.
If there is a vacuum leak that is affecting the idle or smooth running of the engine, it will be in one of the two hoses that connect the ICV. They get hard and loose on the connectors over time. The pipe to the right of the unit is easy to swap, the one to the left that runs down and under the intake stuff is a three handed job to replace.
Automatic transmission, yoyo with that. Can't help you.
It might be your ignition but I'm not convinced from the symptoms you are describing. The rotor arm and contact points do wear but I would have thought the engine is more likely to be missing rather than stalling if that's the case.
As for the flat battery, check the voltage across the terminals with the car running, it should be around 13.5v if the alternator is working. If its less than that, there's your culprit. If you're lucky it will be worn brushes, which are easy to replace, if not you need to replace the alternator. There's some good info on this if you search, I'm in the middle of the same problem with our 230 as we speak and found out all I needed to know here
http://www.peachparts.com/shopforum/search.php?searchid=748096
Hope this helps and good luck getting it fixed.
Benz-lgb: the part circled in red is the Fuel Pressure Regulator, its function is to maintain fuel pressure in the CIS system. Although there is a hose to siphon off fuel if there is a leak in the diaphragm, I understand that they rarely malfunction. Unless you get water in your petrol, in which case they will end up in the bin with all the other expensive bits of injection system.
