Extract all places as nodes with their corresponding admin boundaries ISO codes

You tackle this problem not by asking one question after another here hoping others will do all the work for you, but by sitting down and creating a solution yourself. Try out those things others have told you in your other questions and play around with it. You have looked at the data already, good! Now try out solutions. When you have tried something, come back with more specific question.

Nobody ever has 100% accuracy. Only you know what you want to use this data for so only you can decide what level of accuracy you actually need and where you are willing to make compromises.

To answer your last question first, there will certainly not be 100% accuracy nor completeness. This starts with the question of "what is a city's respective admin boundary"! For many countries you will not even have all city nodes, much less admin boundaries on the municipal level.

If I were asked to generate this data set, I would

1. import planet into osm2pgql (possibly with a reduced dataset like you asked about earlier)
2. where there are polygons with a place=city tag, compute a point on surface (not centroid)
3. for each place=city node and each node found in step 2, find the smallest enclosing admin boundary of admin_level 8 or smaller; if that admin boundary is not of admin_level 8 (but smaller) then ensure that no other place=city nodes are in the same area (else drop it)
4. de-duplicate the list created in step 3 since step 2 might have introduced a place=city node that was already there