Short answers, pulled from the story.
Passover is a literal English translation of the Hebrew term Pesach, first recorded in English in William Tyndale's translation of the Bible. The Hebrew verb pasach refers to God passing over or skipping the homes of the Israelites during the tenth plague of Egypt, though the Targum Onkelos translates it as coming from a root meaning to have pity.
Passover begins on the fifteenth day of the Hebrew month of Nisan, which falls between March 26 and April 25 on the Gregorian calendar; in 2027 it begins at sundown on Wednesday, April 21. In Israel it lasts seven days; Jews outside Israel in Orthodox and Conservative communities celebrate for eight days; Reform and Reconstructionist Jews observe seven days.
Chametz is any leavened food made from one of five grains combined with water and left to sit for more than eighteen minutes. The Torah forbids eating, owning, or possessing chametz during Passover; observant Jews spend weeks beforehand cleaning their homes and may sell chametz through a rabbi rather than destroy it.
The fifteen parts of the seder, as structured by the Haggadah, run from Kiddush and the first cup of wine through hand-washing, dipping of karpas, breaking the matzah, retelling the Exodus with the four questions, a second hand-washing, blessings and eating of matzah and maror, the holiday meal, eating the afikoman, grace after meals with the third cup, Hallel with the fourth cup, and a concluding Nirtzah. The fifteen parts parallel the fifteen steps in the Temple in Jerusalem on which the Levites stood.
The afikoman is the larger piece of the middle matzah broken during the fourth part of the seder, called Yachatz. It is set aside and must be eaten as the final item of the meal in the twelfth part, Tzafun; under the Mishnah it substitutes for the Passover sacrifice. Many families keep children engaged by hiding the afikoman and offering a prize for its return.
The Counting of the Omer begins on the sixteenth of Nisan, the second night of Passover, and continues for fifty days until Shavuot. Each evening, men and women recite a blessing and count the day aloud; the count marks both the agricultural transition from barley to wheat and the spiritual journey from physical freedom at the Exodus to the receiving of the Torah at Mount Sinai.