The three most commonly accepted English language phrases used when referencing a generational group such as you described are "the current generation," "the present generation" and "today's generation." All are equal in formal definition and none has shades of meaning. Each is correct for all situations. (Certain very specific situations may require slight changes. I will give the circumstances further on).
Additionally, the phrase "most recent generation" may be used when emphasizing differences from earlier generations. Its use is entirely optional; any of the other three phrases remains perfectly acceptable.
In American-dominated Western culture, it has become standard convention to establish a commonly agreed-upon name for each generation, beginning with the group born during the late 19th Century which came of age at the time of World War I. They were known as the "lost generation," acquiring the name from American poet Gertrude Stein. A web search for "generation names" will provide a list. As a consequence, if the certain country you mentioned is Western in orientation, you have the option of using Western names. For non-Western societies, that is obviously inappropriate.
Note also that a Western readership expects a certain idiom be applied when referring to non-Western generations. This idiom is subtle, with most native speakers unaware of its existence; nevertheless, they are so familiar with named generations that they expect one be provided. It only need be provided once, on first reference, and in the form of a journalistic appraisal. Thereafter, the commonly used phrases are appropriate. Usage examples are "the present generation of Negombo Tamils" and "the current generation, which has never experienced peace."
To answer your second question, a word which refers to a group and which ends in -tion is always singular in number. For example, one would say "Our nation is," not "Our nation are." Such words, however, behave in the standard English manner and become truly plural in number when the letter 's' is added, so one would say, "The nations of the world are."
