Short answers, pulled from the story.
The word country entered English after the Franco-Norman invasion during the 11th century. It arrived from Old French which derived from Vulgar Latin terms meaning land lying opposite or spread before.
The 1933 Montevideo Convention outlined four criteria for statehood including permanent population, defined territory, government, and ability to enter relations with other states. Article 1 of this convention describes a state as a person of international law.
Estimates range between 193 to 237 depending on how one counts disputed territories. No universal agreement exists on the number of countries in the world today.
Widespread use of flags outside military or naval contexts began only with the rise of nation-state ideas at the end of the 18th century. National flags came to represent most European states during the 19th century as nationalism became common across the continent.
The World Bank Atlas method classifies countries as low-income, lower-middle-income, upper-middle-income, or high-income economies. For the 2020 fiscal year low-income economies had GNI per capita of $1,025 or less in 2018 while high-income economies exceeded $12,376.