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1)

(a) The Gemara understood that, when the Mishnah writes that the baby born after the Sandel is not a Bechor, it is referring to the baby which is subsequently born. But that makes no sense, asks the Gemara, because we do not need the Sandel to exempt the baby that is subsequently born from the Bechorah; It is exempt anyway, because of the baby that was born together with the Sandel?

(b) The Gemara answers that we are referring, not to the subsequent baby, but to the baby that is born together with (and which is responsible for), the status of the Sandel - and we are speaking when the Sandel was born first.

(a) The Mishnah needs to tell us that the woman must bring a Korban for the Sandel, when the other baby was a Yotze Dofen, and does not require a Korban.

(b) According to Rebbi Shimon, in whose opinion a Yotze Dofen is Chayav a Korban, the Mishnah speaks in a case, when the first baby was born at a time when she was about to convert, but had not yet done so, and the Sandel afterwards.

(a) If the two babies are wrapped together, how is it humanly possible to convert in between the birth of one and the other?

(b) When the Beraisa writes that they are wrapped together, it must not be understood literally, but merely that they are close to each other, the head of the second baby resting on the stomach of the Sandel; in fact, the other baby pushes the Sandel with its head, so that, in the case of Bechoros, where they emerge head first, the Sandel is the first to emerge; whereas in the case of Chiyuv Korban, which speaks when they come out feet first, it is the live baby which comes out first.

(c) Rava establishes the Beraisa literally, when the two babies were actually lying beside each other, and the two Mishnahs speak in the reverse order that we learnt earlier: the Mishnah of Bechoros speaks when they emerged feet first; the second baby, which has life, holds back, the Sandel, which does not, therefore emerges first.
The Mishnah of Korban speaks when they came out head first, at exactly the same moment; the live baby is called born as soon as its head emerges, whereas with regard to the Sandel we have learnt that 'Ein ha'Rosh Poter bi'Nefalim', so that the Sandel is not yet considered born. Consequently, it is the other baby which is born first.

(a) Rebbi Shimon holds that a Shilya is not a sign that there is a baby, because, in his opinion, there may have been a baby which melted.

(b) A Shilya initially looks like the Areiv-thread (the warp) of the weaving-loom; ultimately, it resembles a Turmus-bean (according to the Tosefta quoted by Rashi, it refers exclusively to the shape of the head.)

(c) Its minimum size is a Tefach, and it is hollow.

(a) The minimum size of a Shofar is one Tefach - four thumb-breadths - sufficiently long to fill the whole hand and protrude at both ends, so that nobody will think that he is blowing through his hands.
The minimum size of the spine of the Lulav that needs to protrude above the Hadas is one Tefach (not counting the height of the leaves that protrude above the spine).
A Sukah must consist of at least three walls, two full-size walls of seven Tefachim, and the third wall at of least one Tefach.
The hyssop used for the purification of a Metzora and of a Tamei Meis must be at least one Tefach long.

(b) The spine of the Lulav is the only one of the five to be a statement of an Amora (Rebbi Yochanan).

(c) Shilo Ish Kefar Tamarta lists two, because, according to him, Eizov is not a Beraisa quoted by Rebbi Chiya, but a statement that Rebbi Chiya issued.

(a) Something which is a Tefach long and a Tefach wide, and is a Tefach from the ground, serves as an Ohel: It transmits Tum'ah from one end to the other - if a Kezayis of corpse is lying underneath it on one side and an article on the other, the article becomes Tamei.
On the other hand, if the article is lying on top of the Ohel, the Ohel will protect it, preventing it from becoming Tamei (which it would not have done, had one of the three specifications been missing).

(b) This case is not included in the list of five because the list only incorporates things which are one Tefach long, but not things which need to be a Tefach long, wide and high from the ground.

(c) The maximum size of a handle of a stove which is Metamei because of Yad, is one Tefach This means that if the stove is Tamei, and there is a loaf of bread on the handle (which is shaped like a small ledge), then the loaf is Tamei too. If it is more than a Tefach, then it does not become Tamei, because , on account of its excessive size, it stands to be cut off. It is not included in the list of five, because the list incorporates only cases whose minimum size is a Tefach, but not those where a Tefach is its maximum size.
Also, because the list only includes cases which are unanimous, and ourMishnah goes according to the Chachamim. According to Rebbi Yehudah. a stone more than a Tefach is only not Mekabeil Tum'ah when the oven is next to the wall, in which case a larger handle will prevent the oven from standing flush against the wall; otherwise it is Metamei.

(d) According to the Chachamim, the minimum size of a stove regarding receiving Tum'ah is one Tefach, because that is the minimum size oven with which small girls play baking.
It is not included in the above list because the list only covers unanimous opinions, not Machlokes, and, according to Rebbi Meir, the minimum size oven to be Mekabeil Tum'ah is four Tefachim.

7)

(a) The list only incorporates Chullin, not Kodshim, which explains why the case of the Aron was omitted.

(b) The list does not include the Koreh of a Mavuy, because it is purely mi'de'Rabbanan, and the list only incorporates those things which are d'Oraysa, but whose Shiur is not mentioned explicitly.

(a) If a woman discharges a Shilya after having given birth to a live baby, then even after ten days, we will still connect the Shilya to the baby, without suspecting that maybe there was another baby. But if the Shilya followed a miscarriage, then we only connect the Shilya with the miscarriage if she discharged it within three days; after that, we contend with another baby, and she must keep fourteen days of Tum'ah.

(b) If a woman sees blood on the eighty-first day after giving birth to a female, she would be Temei'ah because of Nidus; In that case, upon seeing again on the eighty-eighth day, she would be a 'Shomeres Yom ke'Neged Yom. However, now that she discharged a Shilya, not within three days, but four or five days after the first birth, we have to contend with the possibility of a second baby born within a few days of the first, the blood that she saw on the eighty-first day must be considered as possibly being Dam Taharah, in which case the blood that she then sees on the eighty-eighth day will Dam Nidus, and she will be Temei'ah for seven days, not just one.

(c) If a woman gives birth to a species which would live (if it were to be born after nine months) and then discharges a Shilya, we connect the Shilya with the baby, and do not therefore contend with another baby; but if the Shilya is discharged after a species which cannot live (such as a a baby with a thigh in the middle), then we do not connect it with the miscarriage, but assume that there was another baby. This Halachah caused Shmuel to be upset with Rav Yehudah, because Rav Yehudah, Rav's ex-Talmid, failed to inform him that Rav had issued such a ruling.

(a) Rebbi replied to the Sha'aleh about a Shilya after a raven, that we would still have to contend with another baby, because we only connect a Shilya with a baby which itself is normally born with a Shilya (such as an animal), but birds do not have Shilyos.

(b) Rebbi maintained that there is no such thing as a Shilya that is attached to a species that does not itself have a Shilya.

(c) But the Beraisa specifically states that if a woman miscarries the form of an animal, a beast or a bird, if the placenta is attached to them, then we do not need to contend with another baby; So clearly, it *can* happen.

(a) The reason that we give the Shilya not attached to the animal, the Chumra of two babies, is because we suspect that both the Shefir of the Shilya and the Shilya of the Shefir melted.

(b) According to the Rabbanan of Rebbi Meir, in whose opinion a miscarriage of any form of animal does not render the woman Temei'ah Leidah, the Chomer Shenei Velados means that we consider the animal as if it had not been born, so she has no days of Taharah, but, on account of the Shilya, we contend with the possibility of a human baby girl, for which she must sit fourteen days of Tum'ah.