You are a lucky man if you can pass visual SMOG test with the metal pipe sticking out...

I'll just reply in order of your email.

The things you've done are fine-gas-30mile drive is fine, but I was told on my late model computer controlled cars to drive them 50 to 100miles. I think you should be okay. Also, you want to go to the smog test right away. Non of this sitting around for 15min to 30min before the actual test.
I'm sure 2500 is around 70 to 80mph with a transmission with overdrive, so on non overdrive transmission it will be around 50 to 60mph. With Mercedes Cars, the overdrive transmission did not arrive until the 722.5 transmission. Your transmission 722.3 or earlier unit. Once your CATS are gone. They are gone. On the RPM, you can run that RPM in park.

The cap and rotor. I would inspect it, and clean them with fine sand paper. Put dielectric grease on the boots of the spark plug wires. I HOPE YOU ARE DOING THE DIY ON THIS CAR BECAUSE PAYING FOR ALL SERVICES ON THESE CARS IS REALLY A LOSING PROPOSITION....

About the idle, it does not really matter, but like all cars of the eight's had a idle damper by a cushion diaphragm, or one controlled by vacuum that has step graduations.

Inspect your vacuum lines and soft rubber unions as they get soggy soft like a marsh mellow if my 1996 had some. YOUR 1983 WILL DEFINITELY HAVE SOME BAD ONES.

The metal pipes, no clue... My guess is the EGR pipe, but it's location is odd. The pipe could be the heat riser from the exhaust to aid in the warming-up of the car. The pipe is generally about three to four inches in diameter, and it feeds into the air cleaner assembly.

The other possibility's:

a) is the fresh air injection into the CATs to aid in emissions burning in the mornings-All modern cars have a electric pump that operates and has a valve to let the air pass. I do not know if such a system was uses in the 80's(definitely not on domestic cars of the time).

b) crankcase gases pipe, but generally these gases are taken from the valve cover threw a one-way check valve called a PVC on the valve cover.

c) the pipe is too wide for it to be charcoal gases recirculation ...

Do the EGR tests your self to qualify the EGR gas system, and to test the vacuum control to the EGR.

Best of luck,

Martin