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1)

(a) If the blood is found on the floor of the Perozdor, the woman is Temei'ah Vaday, because Rebbi Chiya goes after the Chazakah, and does not contend with the possibility that the blood may have flowed from the Aliyah when she lay back.
On the other hand, there where the blood was found on the roof of the Perozdor, the fact that it was found on the roof (which is closer to the Aliyah) cancels out the fact that it was at the back (which normally makes it more likely to have come from the Cheder), making it Safek Tamei.

(b) Abaye, unlike Rami bar Shmuel and Rav Yitzchak b'Rebbi Yehudah, gives a reason for his opinion: he explains how we contend with the possible suspicion that she may have bent forward or lay on her back, it will also be a Safek if the blood is found on the floor of the back of the Perozdor, and can under no circumstances conform with the opinion of Rebbi Chiya.
(According to the Lashon of Abaye that we always follow the Chazakah, the Gemara has already explained how that statement actually does support the opinion of Rebbi Chiya.)

(a) If there is a 'Shilya' (a placenta) in the house, then the house is Tamei with the Din of Ohel ha'Meis, because the majority of Shilyos come with a baby.

(b) If a woman gives birth to a fully-developed hand or foot, then she is Temei'ah Leidah, and must keep the Yemei Tum'ah of a female, and the Yemei Taharah of a female. That is because by most births of this nature, the limb comes from a complete baby which disintegrated, and for which she is Temeiah. In spite of the fact that in a minority of cases, the limb was independent, she is nevertheless Temei'ah Leidah with a Din Vaday.

(c) What all the cases have in common, is that if Terumah became Tamei through them, it has to be burnt - which is the major distinction between Vaday Tamei and Safek Tamei.

(a) If someone buys a piece of meat from a shop in a town where nine shops sell Shechted meat, and one shop sells Neveilah, and he cannot remember from which shop he bought, then the piece of meat must be considered Neveilah, because he bought it from a shop whose location is fixed - and that is where the Safek began.
If however, he found the piece of meat lying on the ground, which is known as 'Nimtza' (found in a Makom Safek), or 'Parush', then it is considered 'Shachut', because 'Kol de'Parush, mei'Ruba Parush'.

(b) Why is this not another example of 'Rov' being like a Vaday (every Rov *le'Heteira* is really a Kashya on Rebbi Yochanan, and 'Tesha Chanuyos' is but the Gemara's example of these)?

(c) The Gemara answers that Rebbi Yochanan knew full well that the Torah considers a Rov like a Vaday, and when he made his statement of 'three places', he was referring specifically to the area of Tum'ah, where, for some reason, Chazal might well have been Machmir, to decree that the Terumah should not be burnt, but not to any other area of Halachah.

(a) If there are nine frogs and one Sheretz lying in one place, and someone touched one of them and does not know which one he touched; the Din is similar to the above: in a Reshus ha'Yachid (where Safek Tum'ah is Tamei), he is Tamei; in a Reshus ha'Rabim (where Safek Tum'ah Tahor), he is Tahor.

(b) However, if the creature that he touched had been moved to a separate spot when he touched it, he is Tahor (because the Din of Safek Tum'ah bi'Reshus ha'Yachid, Tamei was not said where there is a Rov).

(c) This is not a Kashya on Rebbi Yochanan, the Gemara explains, because Rebbi Yochanan was referring exclusively to the Tum'ah *of a woman*, not to any other Tum'ah.

(d) Nor is there a Kashya on Rebbi Yochanan from Rebbi Yehoshua ben Levi (who considers an unidentified miscarriage a definite baby due to a 'Rov'), because he is an Amora, and Rebbi Yochanan was referring exclusively to Mishnahs and Beraysos.

5) If we were to explain Ravin's statement as meaning that the Beraisa in question is not only not a disproof to Rebbi Yehoshua but is even a proof, then we would have another Beraisa to conform with Rebbi Yochanan, and there would be four, not just three.
Therefore we are forced to explain that the Beraisa is neither a disproof, nor a proof.

6)

(a) Rebbi Meir says most children play with Sheratzim, and are therefore Tamei, but there are a few who do not. Add that to the Chezkas Taharah of the piece of dough which the child is holding, and you have two against one (the Miy'ut plus the Chazakah are stronger than the Rov). Consequently, the piece of dough is Tahor.
The Chachamim say that we do not contend with the Miy'ut when there is a Rov, and the dough is therefore Tamei.

(b) Rebbi Yochanan holds that Terumah which touches the piece of dough is not burnt (because Rov is not ke'Vaday).
Clearly then, when Rebbi Yochanan lists three cases where Rov is ke'Vaday, he is not coming to exclude Rov against Chazakah, since he has already issued that ruling there, and would not need to repeat in the form of an inference.

(c) The solitary case that Rebbi Yochanan comes to exclude is that of a woman who gives birth to a piece of flesh, which, according to the Tana Kama, renders her Tamei (because of Nidus, only if blood accompanied it), but in the opinion of Rebbi Yehudah, it renders her Tamei anyway. And it is Rebbi Yehudah's opinion that Rebbi Yochanan is coming to qualify. Yes, she is Temei'ah, he says, but not to be Metamei Terumah to the point that it has to be burnt - like the other three cases of Tum'ah by a woman, mentioned above.

(a) In the opinion of Rebbi Yochanan, Rebbi Yehudah declares the woman Temei'ah whether the piece of flesh resembled the color of the four colors of Dam Tamei or not.

(b) In fact, the Gemara explains that the Tana Kama agrees that if the piece of flesh resembles the four colors of Dam Tamei, that she is Temei'ah, even if there is no blood; and Rebbi Yehudah agrees that she is Tehorah if it does not (since then, it can hardly be a blood-clot). Their Machlokes is confined to a case where the piece actually got lost; Rebbi Yehudah goes after the majority of pieces of flesh, which resemble the color of blood, whereas the Tana Kama does not.