You do not have to disconnect the speedometer cable at the transmission on this model. Remove the kick panel under the dash. To do this, remove three small screw covers by prying them out, then remove the three phillips screws. Then release the grey plastic phillips looking fasteners below the panel, one on each side. Release these grey plastic fasteners by turning them 1/4 turn either direction and then pull or pry them out.
After removing the lower panel, you will be able to reach behind the instrument cluster and push it out. You will also be able to disconnect the speedometer cable. You will need to disconnect the 10MM oil pressure line to the guage. Don't forget to back up the line connection with another wrench to prevent damage to the oil pressure guage.
There also is a round black connector with about 10 or 12 wires that connects to the cluster. You will also have to remove a few other single connectors, paying attention to where they go, so you can reconnect them correctly.
Once the cluster is on the bench, check the potentiometer, the brightest setting isn't half bright enough, so if the potentiometer is bad, don't hesitate to jump it, just use an ohmmeter and think it through, before you solder anything in place. If all the bulbs are out, you will probably find the potentiometer to be the problem.
On cold starts, the engine will run rough for a little while. On the 240D there is a manual idle speed adjuster, but there is none on the 300D. It could be that there is some automatic idle adjuster, but I don't think so. This model has pin type glow plugs, which I have found only last a few years, in your climate they may not last that long. If you have any starting problems, a glow plug change is always in order, they are inexpensive and easy to change.
I have never added ATF to the tank, but I doubt that it would hurt anything. There are plenty of quality additives that would probably do a better job.
The manuals are available from several sources, I'd start with the parts shop on this site. They have a CD that's very complete.
'84 Euro 240D, 516K miles
'88 300E 5 Speed
'81 300D Daughter's Car
Over 800,000 miles in