Laws and Customs of Chanuka
The Holiday of Chanuka is of rabbinical origin. As such, the question arises: How can we say, “That (G-d) sanctifies us with His mitzvot”? Where in the Torah is there a command to light Chanuka candles? Our Talmudic Sages in Tractate Shabbat (23a) ask this question and answer: It is written, “You shall do according to the word that they (the Rabbis) will tell you... According to the teachings that they will teach you and according to the judgment that they will say to you, shall you do; you shall not deviate from the word that they will tell you, right or left” (Devarim 17:10,11). Since the Torah commands us not to deviate from the words of the Sages, it follows that when they decreed that candles are to be lit on Chanuka it is as though the Torah commands us to do the mitzvah. (Ta’amei Haminhagim 844)
Why do we say the complete Hallel prayer on each of the eight days of Chanuka? One reason is that each day that the oil burned there was a new miracle added to the one from the day before (Mishneh Berurah 783:1). Another reason offered is because on each day we add an additional candle (Avudraham).
The reason the Rabbis instituted lighting Chanuka candles in the Beit Haknesset is for travelers who did not have a house to light in. This is similar to the custom of making Kiddush in the Beit Haknesset on Friday night, which was originally established for travelers who ate and drank there. (Lavush 681:8)
On the first night of Chanuka three blessings are recited: “To light the Chanuka lights...”, “Who has performed miracles...” and “Who has kept us alive....” One who forgot to say the blessing “Who has performed miracles” on the first night should say it the second night (when lighting or while the candles are still lit), or when he remembers (even on the first night as long as the candles are still lit. (Shulchan Aruch Orach Chaim 676:1; see Kaf HaChaim)
Someone who did not light on any of the nights, and does not plan to light that night, should make the blessing “Who has performed miracles”, and on the first night also “Who has kept us alive” when he sees the Chanuka lights. This rule applies only when he does not have someone else lighting for him. (Shulchan Aruch Orach Chaim 676:3)
We don't mention Chanuka or Purim in the “al hamichiya” after-blessing said after eating foods made from the five grains, such as cakes and pastas (other than bread), since these holidays are not mentioned in the Torah. (Machatzit HaShekel 208:18)