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1) The Gemara's final ruling is that a woman who is able to make Chafifah by day, is obligated to do so, and it is only on Motzei Shabbos (because it is not possible to make the Chafifah on Shabbos), that she is permitted to make it by night just before the Tevilah.
(See also Tosfos, who learns that both 'Efshar' and 'Lo Efshar' refer to Motzei Shabbos).

2)

(a) Since the woman made a Bedikah on the seventh day, she has a Chezkas Taharah, so that, Taharos with which she dealt, between the Tevilah on the night of the eighth day and her discovery of blood a few days later, remain Tahor.

(b) In this case, where she discovered blood on the seventh day, then, even if she found no blood after her Tevilah, she has a Chezkas Tumah, and all the Taharos that she dealt with after the time that she discovered blood, will be Temei'ah.

(c) The woman's Chezkas Taharah in (a), will not however, help her, as regards being Metamei retroactively Mei'es Le'eis, whenever she sees blood after her Tevilah - only between the Tevilah and the Mei'es Le'es before she found blood. That speaks if she had no Veses; but if she did, then her Veses helps to say 'Dayah Sha'tah', and she is Tehorah right up to the time that she saw.

(d) Rebbi Yehudah holds that the woman's Hefresh be'Taharah is only effective if she did it after Minchah ( Bein ha'Shemashos ), but not during the day.
Whereas according to the Rabbanan, even if she made the examination on the second day, it also helps - Bedieved - to give her a Chezkas Taharah.

(a) The Reisha of our Mishnah describes a woman whose final examination took place on the seventh day, as having a Chezkas Taharah, so how can Rav say that she is Vaday Temei'ah.
And as far as the Seifa is concerned, the Mishnah is speaking of a case when the last examination found the woman Tehorah, so there too, how can Rav say that she is Vaday Temei'ah?

(b) Consequently, the Machlokes between Rav and Levi must be an independant one: It speaks when she inspected herself on the seventh day and found that she was Temei'ah, and then again at a later date, she was Temei'ah. However, she did not make her final inspection at the Bein ha'Shemashos at the end of the seventh day.
Rav holds that, since, by her final inspection during the seventh day, she was Temei'ah, and then she was again Temei'ah, a few days later, we assume her to have been Temei'ah all the time, and she is Vaday Temei'ah. But according to Levi, she is only a Safek Temei'ah, because who can say that she did not stop seeing at Bein ha'Shemashos at the end of the seventh day, and that the blood which she saw later was not a new sighting?

4)

(a) Rava says that a woman is not Metamei Mei'es Le'es during her days of Zivus.

(b) Even if we did refute Rava above, that does not mean that we cannot ask on him from *our* Mishnah, as well.

(c) Rava would answer this Kashya by connecting the words 'u'Metamei mei'es Le'es' (not to *our* Mishnah, which speaks about the end of the days of Nidus, going into Zivus,) but to the first Mishnah in the Perek: namely, that of 'Ra'asah ve'Odah be'Veis Aviha', where Beis Hillel give her the whole night; should she then see blood, she will be Temei'ah retroactively 'Mei'es Le'es or mi'Pekidah li'Pekidah'.

(d) We might have thought (in the case of 'Ra'asah ve'Odah be'Veis Aviha') that, since she had a few days of Taharah, she should, when she sees blood the next time, have the Din of a Besulah, and we should therefore say 'Dayah Sha'atah'. Therefore the Tana teaches us that we nevertheless say Mei'es Le'es' etc.

(a) According to Rav Huna bar Chiya quoting Shmuel (who maintains that a woman cannot fix a Veses during her days of Zivus), how can the Mishnah write, with regard to a woman who sees after the termination of her Nidus (which means that it is during the days of Zivus) 've'Im Yesh Lah Veses, Dayah Sha'atah'?

(b) When Shmuel said that a woman does not fix a Veses during her days of Zivus, he meant that the Veses that she fixed then can be easily changed, just through one sighting on a different day (instead of the three sightings that one normally needs to change a Veses). But if she had a Veses during her days of Zivus, then we would certainly say 'Dayah Sha'atah' - not to be Metamei her Mei'es Le'es (even more so than usual, since she has a Chazakah of being a Mesulekes Damim).

(a) Even Rebbi Yehudah has to admit that she does not inspect the entire Bein ha'Shemashos, only during a part of it - leaving open the possibility that she may have seen blood after that; nevertheless that inspection renders her Tehorah, and we do not suspect that maybe she saw afterwards. In that case, why does he not also admit that whenever she inspected last during the seven days without finding blood, it should suffice to render her Tehorah after the seven days (i.e. we ought to assume that she did not see between the last inspection and the end of the seventh day).

(b) At the time when Rebbi asked Rebbi Yossi and Rebbi Shimon about the other days, he assumed that a Bedikah on the first day is not sufficient to be Metaher her, because on the first day, she has a Chazakah of Ma'ayan Pasuach.

(c) He concludes however, that, had he asked Rebbi Yossi and Rebbi Shimon about the first day, they would have ruled there too, that the woman is Tehorah.

(a) Rebbi Yehoshua maintains that a Zavah who examined herself on the first and seventh days has only two clean days to her credit.

(b) Whereas according to Rebbi Akiva, she has only one day (the seventh); the reason for this, is because Rebbi Akiva requires seven (consecutive) counted days.

(c) Rebbi Eliezer asks Rebbi Yehoshua from "Achar Tithar" etc., that she has to have seven clean days, without any days of Tum'ah in between, and in our case, five days of Safek Tum'ah interrupt in between the two days of Taharah?

(a) We see, asks Rebbi Yehoshua, that there are occasions when there are days in between which are not counted in the seven clean days (such as a Zav who saw Keri, who breaks that day, and a Nazir who went under branches and ledges which are a Safek Ohel), yet they count the days before and after the two events - in the clean days of a Zav, and together with the other days of Nezirus (respectively). So why should the Zav whose five middle days are a Safek, not do likewise: to count the second and the seventh days only.

(b) Rebbi Eliezer's real reason is, because if one is permitted to count the days, ignoring the days which are a Safek, one will confuse this with the days when one is a Vaday Zav, and ignore those and count the other days (which of course is unacceptable, since Vaday Zivus definitely breaks all the counted days).
But this is not the case by Keri, which nobody will confuse with Zivus (to think that, just as Keri does not break the counted days, neither will Zivus); nor by Sechachos and Pera'os, which are not proper Ohalim, and nobody will confuse them with a regular Ohel (to say that, just as Tum'as Ohel that comes through Sechachos and Pera'os does not break the days of Nezirus, neither will Tum'ah that comes through a real Ohel.

(c) Although in principle, Rebbi Yossi and Rebbi Shimon consider the opinion of Rebbi Akiva more logical than that of Rebbi Eliezer, they agree Halachically, with Rebbi Eliezer, to include all seven days in the count of clean days (presumably because they had received this be'Kabalah - traditionally - from their Rebbes).