Hallo, Vadim. The word 'the' is known as a 'definite article' (not a toponym, which is something else entirely). In English we have definite ('the' is the only definite article in English) and indefinite articles ('a' and 'an').
Yes, you chose correctly in each of the examples above, in other words all your answers are correct. However, the correctness of your answers has nothing to do with whether or not something is 'on the ground', as you put it. It has to do with whether or not the name of a thing or place (the noun) has been 'qualified' in some way, using an adjective or adjectival clause, or a phrase, OR if you are indicating something generally or specifically. So in the case of a country or place, you would for example say: 'I spoke to friends from Germany' but you would say 'I spoke to friends from THE Federal Republic of Germany.' Also, you would say: 'I spoke to friends from England/Britain ', but 'I spoke to friends from THE United Kingdom/UK.' Or 'I spoke to friends from America' but 'I spoke to friends from THE United States'.
In the case of nouns like 'corn', if you are referring to corn in a specific way (talking about a specific thing, e.g. THIS corn), you would use the indefinite article 'the', to indicate for instance the corn on your plate, or corn from a particular place, etc. If you are talking about corn generally, e.g. the fact that you ate corn while you were on holiday, or prefer maize to corn, for example, you do not need the article 'the'.
So you would say: 'I ate corn all holiday' but 'I ate THE white corn' OR 'I ate THE corn they gave me.'
I hope this is helpful. If you have any further questions about this, you are welcome to ask.