Short answers, pulled from the story.
A city-state is an independent sovereign city that serves as the primary hub of political, economic, and cultural life within its contiguous territory. This concept stands in contrast to that of a regular state or country which typically encompasses a capital city and additional urban centers in addition to the countryside.
Historical city-states included Sumerian cities such as Uruk and Ur along with Ancient Egyptian city-states like Thebes and Memphis. The Phoenician cities included Tyre and Sidon while five Philistine city-states operated along the coast. Berber city-states of the Garamantes thrived in North Africa and the city-states of ancient Greece were known as poleis such as Athens Sparta Thebes and Corinth.
The impasse regarding Rome resolved in 1929 through Lateran Treaties negotiated by Italian dictator Benito Mussolini. These treaties recognized Vatican City as an independent state with the Pope as its head. The Vatican City State has its own citizenship diplomatic corps flag and postage stamps.
Singapore Monaco and Vatican City are the candidates most commonly discussed as modern city-states. Singapore is the largest and most populous city-state in the world with full sovereignty international borders its own currency a robust military and substantial international influence in its own right. The Principality of Monaco borders France as a very small independent city-state.
In the Holy Roman Empire between 962 and 1806 over 80 Free Imperial Cities came to enjoy considerable autonomy in the Middle Ages and in early modern times. International law buttressed their status following the Peace of Westphalia of 1648. Three Hanseatic cities Bremen Hamburg and Lübeck pooled their economic relations with foreign powers.