1) When we finish reciting Hallel on Rosh Chodesh or on Yom Tov, the "shliach tzibur" then says "kadish sho'leim." When we finish Hallel on Chanukah, on the days that are Rosh Chodesh, or Shabbos even when it is not Rosh Chodesh, the "shliach tzibur" likewise says "kadish sho'leim." On the days of Chanukah that are neither Rosh Chodesh nor Shabbos he only says "chatzi kadish." Why?
2) There are two customs regarding the reading of the Torah from the second day of Chanukah onwards. The Tur and M'cha'beir O.Ch. #684 posit that the Yisroel, "shlishi," reads the same verses as the Kohein, beginning from, "Ba'yom hasheini," and so on until the eighth day. The Ram"a posits that the Yisroel reads from the following day, "Ba'yom hashlishi." What is the source of their disagreement?
3) Even when one is delayed and is not able to kindle Chanukah lights in the preferred half hour before "ad shetichleh regel min hashuk," he must light even until the morning. This is so because of opinions that he still will accomplish "pirsu'mei nisa," publicizing the miracle of Chanukah. The lighting is accompanied by the regular "brochos." Shouldn't the lighting be done without the blessings, as per the ruling "so'feik brochos l'ho'keil"?
4) The gemara Shabbos 23 relates that Rabbi Zeira would give a few coins to his host to become a partner in his Chanukah lights. How is this effective? The gemara B.M. 46b says that our Rabbis instituted that paying money to enact a purchase of movable objects is not binding.
5) Chanukah lights are "the light that illuminates the darkness." Obviously, this is to be taken on a spiritual level. The lighting for one particular day is especially "the light that illuminates the darkness." Which day is this, and why?
No doubt, you have noted that "kadish sho'leim" is said after Hallel on days that have Musof prayers, and "chatzi kadish" when there is no Musof, which takes place only on some of the days of Chanukah. But the question remains, WHY? A preface is required. Full "kadish" is required after the "amidoh." If so, why isn't it recited immediately after the "shliach tzibur's" repetition, or at least after "tachanun"? The answer is that if it were said earlier some people would leave davening right after "kadish sho'leim." They would not leave before "kadish sho'leim" because it is a strong, beseeching prayer that our "amidoh" be accepted, "tiska'beil tz'los'hone ……," basically, part and parcel of the "amidoh." Our Rabbis were very interested in having people recite "Ashrei uvo l'Tzion" with a minyan because it is fashioned after "p'su'kei d'zimra," the "amidoh," and includes prayers for the coming of Moshiach bb"a. When we have Musof, people will remain anyway, to daven Musof with the minyan.
(Mahar"i Chalavoh preface to parshas Va'yeitzei)
His words have been very shortened here and they deserve a careful reading.
1) It is based on the same disagreement as on Sukos, whether it is proper to be repetitive. In O.Ch. 663:1 the M'cha'beir says that outside Eretz Yisroel the order of the four "olim" on the first day of "cholo shel Mo'eid," the third day of Yom Tov, is as follows: The Kohein reads day two, the Levi day three, Shlishi repeats day three, Rvi'i repeats days two and three.
The Ram"a differs by Shlishi. He says that day four is read. Commentators explain that the essence of their disagreement is whether it is preferable to repeat Levi and "shlishi" rather than reading the fourth day, which is irrelevant to the day even with "sfeika d'yoma" taken into consideration (M'cha'beir), or if it is better to avoid repetition (Ram"a). The same positions follow through here by Chanukah.
2) The Ra"n and Rambam disagree whether the respite from warring began on the 24th (Ra"n) or the 25th (Rambam) of Kislev. If it began on the 24th, then the second day of Chanukah was the third day of respite. If so, besides reading of the dedication of a corresponding day, i.e. the second day of Chanukah requires reading the "chanukas haMishkon" offerings of the second day, it is also in place to read the third day as a remembrance of the third day of respite, and so on (Ram"a). If we posit that the respite began on the 25th, then the second day of Chanukah was only the second day of respite and there is no place for reading about the third day (M'cha'beir). (Responsa Arugas Habosem O.Ch. #200:3)
The blessings are part and parcel of the lighting because if one were to light without reciting the blessings it would appear as if he is simply lighting for his personal illuminating needs. (Mor Ukzioh)
1) Originally, on the Torah level, money was effective to create a binding transaction. When the Rabbis negated this, they did not negate transactions that were done for the fulfillment of a mitzvoh (see Ch.M. 199:3 Ram"a and Biur Halacha O.Ch. at the end of #656).
2) The reason the negation of monetary payment for an object was enacted was to protect the purchaser, as his object might remain in the domain of the seller for a while, until it is convenient for the purchaser to take it. In the interim, if a fire would break out, the seller might not bother trying to save the item. Since here Rabbi Zeira was only a partner in the item, and not the total owner, money is effective, as there is no fear that the seller would leave it in a fire, as he too has partial ownership in the item.
3) Since this ruling was enacted for the benefit of the purchaser, he can opt out by stating that he will do without the Rabbinical "favour." Here, where it involves the fulfillment of a mitzvoh, even if not verbalized, it is obvious that this is his intention.
Contrary to the questions raised in Chamishoh Mi Yodei'a on the parshios, which appear in the order of the verses to which the questions relate, these five questions on Chanukah have no particular order, save this one. It is specifically the 5th question because the answer is the 5th day. This is because the 5th day of Chanukah can never fall on Shabbos. Shabbos in its own right is an illumination from the darkness of the worldly activity-filled existence. Every other day of Chanukah has a connection to Shabbos, as in one year or another it will land on Shabbos. The 5th day is always connected to the six weekdays. When we light the Chanukah lights for the 5th night it is an "illumination" on the darkest day of Chanukah. The greater the darkness, the greater is the illumination. (Admor of Lubavitch)
A FREILICHEN LICHTIGEN CHANUKAH!