Pick a country at random for a quiz round, a travel challenge or a research prompt, without repeats inside a single draw.
A random country is a constraint, and constraints are what make an open-ended task startable. For a quiz it sets the round. For a travel challenge it removes the endless shortlisting that stops trips being planned. For a research or writing prompt it forces you somewhere you would not have chosen, which is the point, left to ourselves we draw from the same handful of familiar places. For a language or cooking challenge it picks the target so the decision is already made before the excuses start.
The no-repeats toggle turns the draw into a shuffled deck: each country comes out at most once per draw, which is what a quiz needs so a round does not ask the same question twice. Switch it off and each draw is independent, which is right when you want a genuine coin-flip each time rather than a sequence. The list here is a spread across regions rather than every sovereign state, chosen so results are recognisable enough to build a round around without the draw constantly landing on somewhere nobody can place.
No, it is a spread across regions rather than the full list of sovereign states, chosen so results are recognisable enough to build a quiz round around.
Not within a draw when no-repeats is on, which is the default. Turn it off for independent draws where repeats are possible.
No. Every country in the list is equally likely, so a small country is as likely as a large one.