Who is the Jewish group in the first century that concentrated on the application of the Torah?

Answer 1

The Jewish group that concentrated on the study, teaching and application of the Torah in every century was and is the Torah-sages and their many disciples, from Abraham down to today.

The word "Pharisees," which is based on a Greek misspelling used by Josephus, doesn't convey the meaning which it should. It actually refers to the Sages of the Talmud. (The Hebrew word "p'rushim," to which he referred, means people of temperance; the opposite of epicurean.)

Josephus talks of three groups among the Jews in late Second-Temple times: Pharisees, Sadducees, and Essenes. This may convey the mistaken impression that the Pharisees were just one "sect" among others, when in fact Josephus himself admits that the Pharisees (Torah-sages) with their disciples constituted the large majority of the Jewish people.

Although the Christian Testament portrays them poorly, in fact the Pharisees were very egalitarian. They believed that all men were created in God's image and that all had the same rights, and the same right to an education, etc. They were devoted to the practicing of kindness, the fulfillment of mitzvot, the study and teaching of Torah and the education of all people, regardless of status in society. They detested hypocrisy and actively sought it out and criticized it whenever they encountered it. The Pharisees were the only movement to survive the destruction of the Second Temple and were the ancestors of modern Judaism.

Our traditional Jewish beliefs today, including the afterlife and the resurrection, are traditions continuing from the Prophets and the Sages of the Talmud ("Pharisees").

The Sadducees were men of politics and secular life. They had abandoned various parts of Judaism; and they claimed no earlier source (tradition) for their attitudes. They harassed the Torah-sages; and, like the miniscule breakaway group called the Essenes, disappeared at the time of the Second Destruction, just as the earlier Jewish idolaters had disappeared at the time of the First Destruction.

Note that there is a common conception that the Sadducees, like the later (and now largely defunct) Karaites, made a deliberate decision to reject the Oral Law and reinterpret the Scriptures.
However, a careful perusal of the Talmud reveals that the Sadducees were actually opportunists who had nothing much at all to do with religion in any fashion. They were lax in Judaism; they were men of politics who weren't interested in Torah-matters.
The group that did (on rare occasions) argue with the Torah-Sages concerning subjects of religious observance, were a tiny sect called the Baitusim (Boethusians), who quickly died out.