1. He is one of the greatest men that have ever lived in America.

(Is this sentence right? What does 'America' mean? Does America mean the USA or South America and North America?)

2. Which person is the man that/which you want to meet?
(Can we use either 'that' or 'which'? Do we have to use 'that' because of the first word 'Which'?)

3. Who that has common sense can behave in that way?
(We can not use 'who' instead of 'that' here, right? Can we use 'that'way,' omitting 'in'?

3.

1. The best phrasing of this idea is this:

He is one of the greatest men who ever lived in America.
The term "America" should refer to the whole western hemisphere, but in common use, it seems to refer only to the US. All the other countries are referred to by their particular names: Canada, Mexico, Belize, Panama, etc.

2. The words "that" and "which" should generally not be used when referring to a person. Use "who" and its forms for that purpose.
Who is the man you want to meet? or Who is the man whom you want to meet? (The second one is a bit awkward, though, with that extra word in there.)

3. The best way to rephrase the idea in this sentence is this, I think: Whoever has common sense behaves in that way. (You can also remove "in" and the sentence will be fine.)

1. The sentence "He is one of the greatest men that have ever lived in America." is grammatically correct. In this context, "America" refers to the United States of America. The term "America" typically refers to the country located in North America, but it can also be used to refer to the entire continent that includes both North and South America. However, in most cases, when people say "America," they are referring to the United States.

2. Both "that" and "which" can be used in this sentence: "Which person is the man that/which you want to meet?" However, the usage depends on the context and personal preference. In this case, since the sentence begins with "which," it is more common to use "that." Using "which" would still be grammatically correct, but using "that" would sound more natural in this particular sentence.

3. The sentence "Who that has common sense can behave in that way?" is not grammatically correct. The correct sentence would be: "Who, that has common sense, can behave in that way?" Here, "that" is used as a relative pronoun to refer to the people being described. It is necessary to include the preposition "in" after the word "behave." So the sentence would be: "Who, that has common sense, can behave in that way?"