..1. What does 'Stake a claim' mean? What does 'stake' mean here?
In the late 19th century, when the American government opened the prairie lands for settlement, the land was divided into "sections", and the settlers had to drive a wooden stake into the section of their choice in order to establish their claim to that section.
2. What's the difference between 'people' and 'persons'?
People is the commoner of the two words and is used in most ordinary contexts. Persons tends to be restricted to legal, official or formal contexts, as in this vehicle is authorized to carry twenty persons.
3. What's the difference among 'state, nation, country'? Does state usually mean like some states in America? They consist of America? However, country is like America? How about nation? Same thing?
State = a nation or territory considered as an organized political community under one government.
Nation = a large body of people united by common descent, culture, or language, inhabiting a particular state or territory.
Country = a nation with its own government, occupying a particular territory.