The problem with the AI handling tactical nukes, precision strikes, cruise missiles, airlifting etc. is, that they appear very lately in the game in a phase when most normal epic games are still finished and therefore not so much observations about the handling of those concepts by the AI in real game play are done and when having a look at those settings by creating a "laboratory environment" with the editor, it is not sure if the AI is behaving like that in the real game.
Until now I have not experimented with Civ 3 land artillery units. The land artillery in CCM and SOE works different to normal Civ 3 land artillery. The collateral damage flag was introduced for land units with the C3C conquest "Fall of Rome" as an additional flag for normal land units (not artillery). So at least it should work for attacks by normal land units with that additional flag.
The screenshot of bombarding Rheims and simultaneously taking out two buildings of a city by a combination of precision strike and collateral damage, was done many years ago, showing the bombardment of a city by an air unit (strategic bomber) done by me and not by the AI.
Yes, the bombing of cities by air units is in accordance with the observations in the German Civ 3 Wikipedia, based on a test in 2013. Air bombardment at first destroys planes and citizens of a city, if there are no planes in the city, ships, citizens and buildings of the city will be destroyed. If there are neither planes nor ships in the city, according to that article units, citizens or buildings will be destroyed. You can find that article
here. So the article is in German, I think the Google translator will do its job in translating it well to the English language. The article holds many more observations about different kinds of bombardment in C3C.