3. Where can I see how many public works have been done in this city?
Honeslty i dont know, if you can have purely precise number for that, and honestly that is kinda not important, since you need them, or you dont
The only real utility of that, is if you conquer some city, and you wonder
Indirectly you can look at happiness, and there are like 4 cathegories, and this is 3rd line, dont remember wording, but i think it contain "public works"..
Second, you can just look at the prize. It cost by default 500, +100 for each public works, +100 for each era. So if you are Renesiance, and prize is 800, it meants its 2nd..
Third, you can infer more or less from the empire size. You can compare if you have more or less than in other cities, take account for Walls and Castles etc.. then more or less you will know.
The problem is that those sources are kinda poluted by other sources, so if you want to know precise number, you need swet your brain a little.
2. Needs of food/production distress - is it sum or minimum of them that I need to maximize in order to reduce distress?
It says what is the total deficit, and how much you need more to get the next breakpoint.
1. Switching of great works bewteen civs - what benifits can it give?
Some buildings require you specific cmbinations to get theming bonus. This bonus is very powerfull, and you always should
put prio1 on getting theming bonus, if you have even number of great works.
Sometimes the theming comment says "If you want to maximize theming bonus you shoud have art of different eras of civilisation different than your own"
So obviously if all your are your own, you need switching.