Short answers, pulled from the story.
Hanukkah derives from the Hebrew verb meaning "to dedicate," referring to the rededication of the Second Temple in Jerusalem after the Maccabees drove out the Seleucid forces in 164 BCE. The name can also be parsed as "they rested on the twenty-fifth," marking the date on which the fighting ceased.
According to the Talmud (Shabbat 21b), when the Maccabees reclaimed the Temple, they found only one sealed container of ritually pure olive oil, enough to keep the menorah lit for a single day. The oil burned for eight days, the time required to prepare a fresh supply, and the sages of that generation declared the eight-day period a festival.
The shammash, meaning "attendant," is a ninth candle on the Hanukkah menorah. Jewish law prohibits using the eight Hanukkah lights for ordinary purposes; the shammash serves as a practical light source so the sacred flames are not used for illumination. It is given a distinct position, usually higher, lower, or to the side of the others.
Fried foods on Hanukkah commemorate the miracle of oil at the center of the holiday. Potato pancakes called latkes are traditional among Ashkenazi families; jam-filled doughnuts called sufganiyot are common among Sephardic and Israeli families. Foods cooked in oil directly reference the small cruse of olive oil that, according to the Talmud, kept the Temple menorah burning for eight days.
Jewish immigrants to America raised the profile of Hanukkah as early as the 1800s to provide a Jewish counterpart to Christmas celebrations that often overlap with the holiday. By the 1900s, Hanukkah gifts and decorations appeared in stores, and by the 21st century the holiday has taken a place alongside Passover as a primary symbol of Jewish identity in North America.
The House of Shammai held that eight candles should be lit on the first night, decreasing by one each night, because the miracle was greatest at the start. The House of Hillel argued for lighting one candle on the first night and adding one each subsequent night, because the miracle grew in greatness each day. Jewish law adopted the position of Hillel, which is the practice followed today.