1968 GTS 340 with Carter AVS 4966S

Hi Mattax, thank you very much for your detailed answer. Here is my reply:

Parts:
Since I am in Austria/Europe parts are pretty hard and long lasting to get (and expensive). So I wanted to change most important parts upfront.

Cooling System:
I will check the cooling system as instructed by you, but i think nevertheless i will need a new radiator or maybe I can get it fixed. From my point of view the car gets really hot really fast but the temp gauge tells something else. Today I am going to check the temp sensor, maybe I can find something. What would you recommend: Fix original radiator (and install electrical fan), replace radiator with e.g one from champion, replace radiator core.

Engine RPM for slow idle:
Might be, but I do not think that there is air bypassing. I guess that the idle mixture screws are not correct. But what is the correct sequence for adjustment? I thought 1.) timing, 2.) rpm, 3.) carb (e.g. idle mixture screw) repsectively combination of 2.) & 3.) but first definitely timing. Do you suggest another approach?

Distributor:
I was/am pretty dumb. I really thought every distributor works best at TDC for idling. I checked and the one I got is not the original one because it has no batches, labels etc. and no vacuum unit. This also means it has a fixed timing, am I right?
I already have a Proform electronic distributor wiht vac unit in the work shop, I will install it (together with new spark plugs) and try again AFTER I took care of the colling system.

Looking forward to your answer!
Thanks again.
Best Chris