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1)

(a) Beis Hillel agree that during the fifth week (when she does not see blood, though she did see every day of the fourth), she is obligated to Tovel each night, in case it is the last of the seven days of Nidah - hence the twenty-eight days become thirty-five.

(b) The days of Tevilah end at the end of the eightieth day - which falls in the middle of the ninth week (59 days) - besides the first three weeks when she did not see at all (21+59=80)

(c) Since the Beraisa needs to list part of the ninth week, (bearing in mind that we are listing weeks) it lists it as a full week (even though, during the latter half of the week she does not really need to Tovel); and, since it has already listed the ninth week when she does Tovel, it completes the picture (bearing in mind that the weeks are all in pairs - 'Echad Tamei, ve'Echad Tahor') by listing the tenth week, when she does not see blood.

(d) Every week that she is Temei'ah, one has to contend with her being a Zavah (except for the fourth week, where she cannot yet have been a Nidah since the birth, and a woman has to be a Nidah before she can become a Zavah). Consequently, the last day of each Tahor week, besides Toveling each night because she is a Tevulas Yom Aruch (according to Beis Shamai - according to Beis Hillel, in any case), she ought to Tovel also by day?

(a) The Beraisa omits the Tevilos of a Zavah because it concerned only with the Tevilos that she Tovels *before* Tashmish, not after.

(b) Yes! Beis Shamai did include the Tevilos of a *Yoledes* be'Zov, but not those of a Zavah only.

(c) Once it reaches the fourth week, the Beraisa deals only with whole weeks and does not concern itself with single days (that is not to say that she is not obligated to Tovel on this, and on the other days that the Gemara discussed - it is just that the Beraisa is not concerned with them, for the reasons given by the Gemara.)

(d) This also answers the Kashya that one could ask on Beis Hillel - why he does not list the first Bein Hashemashos when the woman returned, which, as we explained earlier, makes up the eighty-fifth Tevilah, according to Beis Shamai.

(a) The Beraisa is not concerned with the Tevilos of a Zavah Ketanah (a woman who has seen one or two sightings) only with a Zavah Gedolah, who has seen three times.

(b) Rebbi Yossi b'Rebbi Yehudah is of the opinion that it is not a Mitzvah to Tovel as soon as the time falls due. Consequently, she can Tovel once on the night of the eighty-first day, and that will suffice to cover all the Tum'os.

(a) A woman who miscarries after forty days does not have to contend with a second birth, since it is impossible to become pregnant again before the forty-first day. Whereas if she miscarried on the forty-first day, she must sit for a male, a female and for Nidus.

(b) According to Rebbi Yishmael b'Rebbi Yossi, a girl is formed inside the mother's womb, only on the eighty-first day, not on the forty-first, corresponding to the eighty days of Tum'ah and Taharah that the mother sits for her (in the same way as a boy is formed after forty days - corresponding to the combined days of Tum'ah and Taharah that his mother sits when he is born).
He therefore maintains that a woman who miscarries on the forty-first day must sit the days for a boy and for Nidus, but not for a girl.

(c) The Mishnah needs to mention that she must sit for a boy, in order that, if she should see - for example - on the thirty fourth day and then again on the forty-first day, she will be Temei'ah on the thirty-fourth, because of the possibility that perhaps she is a Nidah, and Temei'ah Nidah again on the forty-first day (and not just a Shomeres Yom ke'Neged Yom), because we now have to suspect that maybe she miscarried a boy, and the thirty-fourth day was still in the middle of her days of Tohar.
(And the same Chumra will be necessary, should she see on the seventy-fourth day and then again on the eighty-first.)

5)

(a) The Rabbanan simply disagree with Rebbi Yishmael. According to them, the formation of a baby has nothing to do with its days of Tum'ah and Taharah.

(b) They cut open the maidservants of Queen Cleopatra, who had been sentenced to death and killed, and they discovered both male and female babies already formed from the forty-first day.

(c) Rebbi Yishmael however, countered that *he* brought a proof from the Torah, which uses a superfluous word - "Teiled" , to add an extra Leidah for females (from the forty-first day to the eighty-first).
Whereas *they* bring a proof from fools (Who says that the girl had not been formed forty days earlier?)

(d) In fact, they had given them a drug that scatters the Zera (forty days earlier) to prevent them from becoming pregnant). Rebbi Yishmael however, maintains that such a drug is not effective by all women, and that there proof is therefore, ineffective.

(a) Rebbi Yishmael demonstrated his point by cutting up other maidservants and where they found babies inside, boys formed from the forty-first day, and girls from the eighty-first (they could see this from the difference in size).

(b) No proof, said the Rabbanan! Who said that the girls not already been formed forty day before?

(c) Rebbi Yishmael counters this by saying that the maidservants had been guarded for the previous forty days, to ensure that they do not become pregnant earlier.
The Rabbanan however, hold of the principle 'Ein Apotropus la'Arayos' - there is no guarantee against adultery. Who can guarantee that the guard himself did not have an affair with them?

8)

(a) 'Niftach ha'Sasum' refers to the baby's mouth, which was shut prior to its birth, and 've'Nistam ha'Pasu'ach' refers to the navel, through which the baby was fed, right up to its birth.

(b) Chazal say that before it is born, a baby's bowels do not function; otherwise it would kill its mother.

(c) The Gemara describes the Neshamah of a baby as a kindled lamp, which enables the baby to see from one end of the world to the other - just like a dream, where one can well be sleeping in Eretz Yisrael, and yet one sees things that are happening in Spain.

(a) "Mi Yitneini ke'Yarchei Kedem, ki'Yemei Eloka Yishmereini". Which days have months, but no years, asks the Gemara? This can only be the months of birth. Hashem guards the fetus throughout the nine month period, and he never has it so good - and this comes across even clearer from the second Pasuk "be'Sod Eloka Al Oholi".

(b) From "la'Pesach Chatas Roveitz" we learn that the moment that a baby is born, an angel strikes him on the mouth causing him to forget all the Torah that he learnt in his mother's womb (Chazal learn elsewhere from the same Pasuk that as soon as he is born, he receives a Yeitzer Hara [see Maharsha]- and the two Chazal seem to be complementary.)

(c)&(d) We learn from "Ki Li Tichra Kol Berech" (which refers to the day of death), "Tishava Kol Lashon" (which refers to the day of birth) that on the day that a baby is born, he is made to swear that he will be righteous and not wicked; and that, even if the entire world tells him that he was a Tzadik (in his previous life - see Maharsha - he should consider that he was a Rasha there); and that Hashem, together with all His servants and the Neshamah that he is now receiving, are all pure, and that he will forfeit his rights to it, if he does not strive to keep it pure, the way it was given to him.