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1)

(a) By adding "Ein Bo Mayim", the Torah implies, that although there was no water in the pit, there *were* snakes and scorpions (Allegorically speaking, this is taken to mean that head which is empty of Torah, is bound to contain harmful thoughts and ideologies.)

(b) The Menorah should be placed within one Tefach of the doorway.

(c) According to the second opinion, the Menorah should be placed on the entrance, so that, when one enters one's house, he is surrounded by Mitzvos - the Mezuzah on the right, and the Menorah on the left.

(a) Shmuel was surprized that Rav Asi should have prohibited the counting of money by a Menorah: 'Does a Menorah have Kedushah', he exclaimed?

(b) Rav Yosef justified Rav Asi's statement, on the grounds that the blood of a Shechted animal doesn't have Kedushah either, yet the Beraisa, commenting on the Pasuk in Vayikra "ve'Shafach - ve'Chisah", writes that one should cover the blood of a bird or of a wild animal (a deer etc.) with the same hand that one Shechted it, and not with one's foot. Clearly, concludes Rav Yosef, this has nothing to do with the sanctity of the object, but with respect for an object with which a Mitzvah has been performed.
(Incidently, according to the Rosh [Si'man 5] it is only casual Hana'ah which one needs to perform close to the Chanukah-lights - such as counting money - which is forbidden, casual benefit which does need close scrutiny, is permitted.)

(c) When Rav Yosef heard that Rebbi Yehoshua ben Levi learnt the prohibition of using the Succah decorations from that of the Chanukah-lights, he exclaimed 'Marei de'Avraham, Tali Tanya be'de'Lo Tanya!' - The Succah decorations are already mentioned in a Beraisa, whereas the Chanukah-lights are not!

(d) No! One may not take down the Succah decorations on Shemini Atzeres (aside from the possible Isur of untying a knot), since the Beraisa specifically forbids benefit from them - 'until 'Motza'ei Yom-Tov ha'Acharon shel Chag'!
And all Beraisos, of course, were written in Eretz Yisrael, where Shemini Atzeres is Motza'ei Yom-Tov.

(e) It is permitted to take down Succah decorations and use them on Succos, if one stipulated before Yom-Tov, that one did not withdraw one's personal rights from them throughout the period of dusk (Bein Hashemashos).

(a) 1. Abaye quoted Rabbah as saying that, although throughout Shas, Rabbah would follow the opinion the opinion of Rav against that of Shmuel (in matters of Isur), these three cases were the exceptions, where Rabbah followed the opinion of Shmuel.
2. Rebbi Shimon permits one to drag a bench along the ground (even though it may just make a groove in the ground), because it may also *not* make a groove, and, since he does not intend to do so, he may go ahead and drag it to wherever he needs it.
(Incidently, the Hagahos Oshri [Si'man 7] points out that Shmuel only permits one to remove Tzitzis from garment to put on another; otherwise, it is forbidden to remove the Tzitzis from a garment. Rashi too, agrees that the obligation of Tzitzis pertains to the garment, not just to the person.)

(b) Rav forbids one to light one Chanukah-light from another, either because of 'Bizuy Mitzvah' (despising the Mitzvah), or because of 'Akchushei Mitzvah' (meaning that one seems to be taking some of the light and the oil - and thereby detracting - from the one lamp, in order to provide the other lamp with fuel). The difference between the two reasons lies in a case when one lights one light *directly* from the other - and not by means of a twig: the first reason will no longer apply, since the second light is in no way inferior to the first (presumably, we are speaking about two *different* Menoros, and not two lights on the same Menorah - where the second light - which was only lit as a Hidur Mitzvah - is indeed inferior to the first). Nevertheless, he appears to be detracting from the oil and the light of the first Menorah, in order to provide for the second Menorah, so in that case too, it will be Asur.

(c) If Rav's prohibition is restricted to using a medium to light the Chanukah-lights, then Shmuel, who argues with Rav, must permit even using a medium lighting one Chanukah-lights from the other (since it is for the needs of a Mitzvah) even through the use of a medium. In that case, how will Shmuel explain the Beraisa, which forbids one to weigh Chulin coins against coins of Ma'aser-Sheni - even if he intends to use the Chulin coins for the Mitzvah of redeeming Ma'aser-Sheni?

(d) It is forbidden to weigh the Chullin coins against the coins of Ma'aser-Sheni, not because of 'Bizuy Mitzvah' (which does not apply when one is in the course of performing a Mitzvah - according to Shmuel) but because he might find the Chullin coins unsuitable, or other coins better than them, in which case, he will have used the Ma'aser-Sheni coins in vain (i.e. without having performed a Mitzvah with them).

4)

(a) If the Menorah was placed from East to West, then it was the second lamp that was called the 'Ner ha'Ma'aravi', because *it* was the first lamp (after the Ner ha'Mizrachi) to be eligible for the title of "Lifnei Hashem" (which the 'Ner ha'Mizrachi' was not), and we have a principle 'Ein Ma'avirin Al ha'Mitzvos'.

(b) The Kohen would enter the Heichal, where he would find all the lights extinguished. He would then clean out all the other lamps, and replace the oil and the wicks for the evening. He would light the Ner ha'Ma'aravi from the Mizbei'ach ha'Olah, and leave it burning until the evening, when he would take out the burning wick and hold it in his hand - or place it in a receptacle - whilst he cleaned out the lamp and put in new oil and a new wick. Finally, he would light the Ner ha'Ma'aravi with the old wick (which he had just lit), and all the other wicks, each one from the lamp next to it, starting with the ones on either side of the Ner ha'Ma'aravi, which he lit from the Ner ha'Ma'aravi. They did not need to use any medium to kindle the lights, because the wicks were long and could be extended from the one lamp to the next in order to be able them in this fachion.

(a) The Menorah was a testimony for the nations of the world that the Shechinah rested in Yisrael, by virtue of the Ner ha'Ma'aravi, which was the first lamp to be lit each night, but the last to go out (in spite of the fact that the wick was the same size, and the same amount of oil was used - as all the others).

(b) Since the lamp-holders were immovable, the Kohen must have used a medium to kindle the one from the other, leaving a Kashya on both those who hold that the Isur of lighting from one to the other is because of Bizuy Mitzvah, and on those who hold that it is because of 'Akchushei Mitzvah'.

(c) Rav Papa answers that it was not necessary to use a medium to kindle the lights of the Menorah in the Beis Hamikdash, since they had very long wicks, which could be pulled across from the one lamp-holder to the other without removing them from their lamp-holders. That resolves the Kashya on those who learn 'Bizuy Mitzvah' .
The problem however, remains according to those learn 'Akchushei Mitzvah'. According to them, even lighting directly from one lamp to the other should have been prohibited, because of 'Akchushei Mitzvah'? This Kashya remains unanswered.

(a) The Gemara concludes that, if we say 'Hadlakah Oseh Mitzvah', one may light one lamp from the other, just as we find by the Menorah of the Mishkan But if 'Hanachah Oseh Mitzvah', then the Hadlakah is not such a Mitzvah, and to light one lamp from the other would therefore be a 'Bizuy Mitzvah'.
(Whether or not, we hold of 'Akchushei Mitzvah', regarding lighting one from the other using a medium, see Rosh Si'man 7, who brings a Machlokes Rishonim reagrding this point.)

(b) Even if Rava would hold 'Hadlakah Osah Mitzvah', he could still disqualify a Menorah that someone is holding, from the Mitzvah, because people will think that he needs the lamp for his own private use (and we have already learnt earlier that, since the very objective of the Chanukah lights is 'Pirsumei Nisa' (to publicize the miracle) it must be made clear to all and sundry that the Menorah has been lit for the Mitzvah, and not for any ulterior motive.

(c) And by the same token, we do not have a proof from the fact that Rava disqualifies a Menorah that one moved from one place to another after having lit it, that 'Hadlakah Osah Mitzvah', because even if he holds 'Hanachah Osah Mitzvah', he will not be permitted to move it once it has been lit, because people will think that he is moving it for his own personal use.

(a) If the Mitzvah is the Hanachah, then why does the Beraisa only obligate one to extinguish the lamp and re-light it? Why does it not add that one also needs to re-place it? This, concludes the Gemara, proves categorically, that 'Hadlakah Osah Mitzvah', and not 'Hanachah'.

(b) The second proof that 'Hadlakah Osah Mitzvah' is from the text of the Berachah, which is* 'Lehadlik* Ner shel Chanukah', and not *'Lehani'ach'* etc.

(c) Having just concluded that 'Hadlakah Osah Mitzvah', it is obvious that a grown up will not be Yotze with the lighting of a Cheresh, Shotah or Katan.

(d) 'Af Hen Hayu be'Oso ha'Nes' means firstly, that the women were saved from a terrible decree that was aimed specifically at them (that following her marriage, every Jewish woman had to spend her first night with the Greek mayor), and secondly, that the miracle was largely due to the efforts of a woman (the beautiful and righteous Yehudis - widowed daughter of Yochanan Kohen Gadol, who hit upon an ingenious and daring scheme which resulted in her ealiminating the Greek king Aliporni).