Fog lights 101: (assuming a factory install) they only work with the low beams on, you need to "pull" the switch towards you one click. Two clicks would also turn on a rear fog in addition to the fronts, but unless you're driving a euro-car, you won't have one. The amber center dot/light in your headlight knob may/may not have a light bulb in it to show that you've pulled to the second detent.

Rotating the knob to the left turns on the "standlicht" which is a single front and rear light for the left or right side of the car.

There should be a paper diagram under the fuse box lid, german on one side and english on the other.

Double-fast blinking is the classic symptom of one burned out bulb on one side (or the presence of a heavy duty bulb instead of a regular bulb). Get the right wattage and filament for your bulbs and you'll be fine. Don't just grab the one that looks like the right size and shape - it might be a double filament brake light (too hot) it might be a heavy duty signal (blinks too fast).

Read your owner's manual, and do a forum search for "wiring diagram" to find a clickable/downloadable pdf for the W123's.

The ignition switched clock could be a few things: bad fuse, crack in the instrument cluster, bad clock. You'd need to do some more troubleshooting.

The stock US-spec 123 headlights are pretty crappy, so some owners modified their fogs into "driving" lights or wired them to come on with the high beams, or with the parking lights. If the previous owner (PO) customized the harness, you're sort of on your own. You can search and review various fog-light threads to research those options.