Your car may have an factory alarm but it is not what most people expect. No flashing lights or horn beep when activated or anything like that. And there is no switch or flashing light inside the car (although it is shown and described differently in the owner's manual--my switch position is a black blank plate). This is how the alarm works in my car from experience, not from the book: When the car is locked, if a door or something is opened without the key unlocking the car, it will honk the horn and the outside lights will flash. An easy way to see it to lock the car with the hood open, then put it down but not quite latched. If you open the hood again, the horn will beep until you unlock the car with the key (guess how I found that out!). I was under the impression that it was on all USA 300E2.8s. It was listed as standard equipment on the window sticker when my car was new.
If the car has a check engine light, it is at the extreme right of the lights at the bottom of the instrument cluster. The lettering can be read with the key off and should show up yellow when the key is first turned on. I bought my 1993 300E2.8 new in Albuquerque in December 1992, it has never been to Califonia but I suppose it could be a "California" model even though there is no reference to that on the stickers on the car.
As far as the idling problem, I had a similar problem about a year ago. It turned on the check engine light and the code given was the right one--the hot film air flow sensor. It is an extremely simple repair but the sensor costs about $250. I replaced it and it has been great ever since. It would run almost normal at anything other than an idle. It would idle at about 500 rpm, the gradually increase to maybe 1200 to 1500 rpm in about 3 or 4 seconds, stay there a few seconds and then drop to a very low rpm. After a cycle or two of this, it would die. Just a little crack of the accelerator and it would be almost normal at around 900 rpm. Normal driving at highway speeds, normal fuel consumption as well.
Cloth seats were not an option in the USA in 1993 that I know of. It was MB tex standard and leather as an option. Power seats with no memory were standard on the USA 300E2.8 but there may have been an option for that. Mine has no steering wheel adjust and but the power adjust may have been an option along with the power seat memory since the memory also adjusts the steering wheel.