Did Rebbi forget what R. Yishmael b'Rebbi Yosi already said in the name of his father?

Maharsha: No. R. Yishmael had said that he has teachings from his father, but he did not yet say them.

Why do we date Romi's conquest of Eretz Yisrael based on years before the Churban?

Rav Elyashiv: This was a sign that Bayis Sheni will be destroyed. There were stronger Simanim 40 years before the Churban - the lottery for the inner goat of Yom Kipur always came up in the left hand, and the doors of the Heichal opened by themselves, to hint that the enemy will be able to enter.

Where is Chanuyos?

Etz Yosef citing Rashi (Avodah Zarah 8b): It is in Har ha'Bayis.

Why can we not say that fines were not enforced?

Maharsha: This is like it says in Avodah Zarah (8b. If not for R. Yehudah ben Bava, fines would not have been enforced, for Romi decreed to kill anyone who gives Semichah (ordination, which is necessary to collect fines) or receives Semichah. R. Yehudah ben Bava gave Semichah to R. Meir, R. Yehudah, R. Yosi, R. Shimon, and R. Elazar ben Shamu'a.)

Why did they cease judging capital cases?

Tosfos: It seems that it was because the Sanhedrin was not in its proper place (Lishkas ha'Gazis). This is astounding. We expound that it must be in its place from "v'Kamta v'Alisa El ha'Makom", which discusses the rebellion of a Zaken Mamrei. It need not be in it its place when he is judged! It is unreasonable to say that all Chayavei Misos must transgress when it is in its place, for even Zaken Mamrei is not liable until he returns to his city and acts like his ruling! We do not find that in capital cases, we must check that the Sanhedrin was in its place when he transgressed! This is difficult.

Daf Al ha'Daf: Mikra Mefurash (Shlach 27) asked, surely the Sanhedrin was not in its place when the Mekoshesh transgressed. Beis Din does not meet on Shabbos! I answer that it was a Hora'as Sha'ah (Sanhedrin 78b). (NOTE: How can we answer for every case of Chilul Shabbos? The Torah said that Beis Din kills for it, even though Beis Din does not meet on Shabbos! - PF) Tosfos (Kidushin 36a) says that one who is not commanded to wear Bigdei Kehunah, Mechusar Begadim does not apply to him, e.g. women. Tosfos (Yevamos 32b) says that a Zar is not commanded about serving b'Tum'ah. We can say here that there is no problem that Beis Din is not in their place at a time when they do not judge.

Tosfos (Avodah Zarah 8b): We expound, as long as the Great Sanhedrin is in its place "Etzel Mizbach Hash-m", then "Shofetim v'Shoterim Titen" to judge capital cases. If the Sanhedrin left, capital cases cease.

Etz Yosef: They saw that there were many murderers, and they could not judge them. They exiled themselves to exempt themselves from judging them (Avodah Zarah 8b). Rashi there explains that they did not want to obligate the murderers' execution.

Rav Elyashiv: They should have judged them, to fulfill "u'Vi'arta ha'Ra mi'Kirbecha"! The Rambam (Hilchos Melachim 3:10) says that a king is authorized to kill all murderers even without clear testimony or warning, or via one witness, and to kill many in one day, if needed at the time. Presumably, this is only if the murder was not judged in Beis Din. If Beis Din exempted him presumably the king may not kill him. A Beis Din that kills once in 70 years is called savage (Makos 7a). Beis Din would have needed to increase Drishos and Chakiros and make all efforts to avoid killing the defendant, like we learn from "v'Hiztilu ha'Edah." Therefore they did not want to judge them, for many killed without warning... and Beis Din would need to exempt the murderer, and then he could kill again. Therefore, they ceased capital cases, and the king was obligated to kill murderers according to the need at the time, even without warning.

Who were Shimon, Gamliel and Shimon?

Rashi: The first Shimon was Hillel's son. Gamliel is Raban Gamliel ha'Zaken. The latter Shimon was among the 10 Harugei Malchus. He was the father of R. Gamliel of Yavneh, who pained R. Yehoshua (Berachos 27b) and feuded with R. Eliezer (Bava Metzi'a 59b).