I don't want to start an oil war, but the viscosities recommended by Mercedes in the late 80's and early 90's was xW-40 or xW-50 for anywhere except if you are in Arctic / sub-freezing temperatures. The 10W-30 is probably a bit thin, at the next change I'd go thicker.
Also, the M103 engine is known for eating valve guides and seals. Keep an eye on oil consumption, if it's worse than 1000 miles per quart, pretty likely you have one or both issues. New seals can buy you some time but if the blue smoke continues, at some point you may need to replace the guides ($$$), or just feed it oil.
Yes, you can drive the car with the alarm going off (a starter lockout wasn't part of the alarm until 1993). Best solution is to disable the alarm, unplug the "Becker" box under the passenger footwell carpet behind the angled partion panel.
Speedometer / odometer MIGHT be fixable with replacement gears. Alternately, buy a used speedometer from a car with the same gear ratio (or "K" number on the sticker on back of the speedo), and adjust the odo to read accurately.
