1) Yes, the Ba'al ha'Me'or seems to agree with the minhag of one day of Rosh Hashanah that existed in Eretz Yisrael until the Chachmei Provence arrived.
2) See Teshuvas ha'Radbaz 4:1165, who writes that the reason why the Rambam instituted in his time that Chazaras ha'Shatz should not be said was because the situation had developed such that Chazaras ha'Shatz was causing the opposite of what it was meant to achieve. Chazal instituted Chazaras ha'Shatz so that people who were not expert at praying themselves could be Yotzei with the Chazan's Chazarah. However, in the time of the Rambam, the decorum in Chazaras ha'Shatz was so bad that people either spoke to their neighbors or walked out of shul. Even somebody who did not know how to daven himself would walk out of shul, as he saw others doing, and consequently he would not be Yotzei the Tefilah at all. In that context, the Rambam said that the Chazan should daven out loud, and that way the non-expert would listen to him and be Yotzei. On the contrary, the Rambam arranged that the original aim of Chazaras ha'Shatz should be achieved.
3) (a) The Talmud Yerushalmi (Eruvin 3:9) tells us that Rebbi Avahu went to Alexandria and required the Jews there to hold the Lulav on Shabbos. The Korban ha'Edah and Pnei Moshe explain that in that year, the first day of Sukos fell on Shabbos. It seems that Rebbi Avahu was in Eretz Yisrael on Rosh Hashanah, and therefore he knew when Rosh Chodesh Tishrei occurred, so he was in a position to inform them in Alexandria with certainty when the first day of Sukos was. Since he knew for sure that Shabbos was the first day of Sukos, it follows that the obligation then to take the Lulav was d'Oraisa, so he suspended the Gezeirah that people might carry the Lulav in Reshus ha'Rabim.
(b) However, Rebbi Avahu's opinion was not accepted by the other Sages of the Talmud Yerushalmi. Immediately after reporting the visit of Rebbi Avahu, the Yerushalmi tells us that Rebbi said that Rebbi Avahu could not carry out this exercise of going to Alexandria every year and consequently it was not acceptable on any year to take the Lulav on Shabbos.
(c) The Yerushalmi concludes that Rebbi Yosi sent a directive to those living outside Eretz Yisrael saying that even though the Sages in Eretz Yisrael had written exactly when Rosh Chodesh occurred, nevertheless you should not depart from the Minhag of your late ancestors of observing two days of Yom Tov.
(d) So, while Rebbi Avahu was not accused of violating a Gezeirah of the Sanhedrin, the Yerushalmi certainly indicates that the Halachah does not follow Rebbi Avahu, because his opinion does not conform with the Minhag; and as we have seen from the Rambam, the Minhag cited by the Gemara is what is crucial.
Further clarification of source:
We mentioned previously the student of the Rif who held that one need observe only one day of Rosh Hashanah in Eretz Yisrael nowadays. We can now say that this refers to Rabeinu Efrayim, the Talmid of the Rif. The Rif ruled that nowadays one must observe two days of Rosh Hashanah in Eretz Yisrael. However, the Rosh (Beitzah 1:4) writes that Rabeinu Efrayim disagreed and maintained that this only applied in the times when they were still establishing Rosh Chodesh by accepting the testimony of the witnesses, but nowadays that we rely on the "Sod ha'Ibur" the entire Eretz Yisrael receives the status of "Beis ha'Va'ad" -- where the Beis Din presided and where no doubt existed when Rosh Chodesh fell, so one needs to observe only one day. The Rosh writes that the Ba'al ha'Me'or also ruled like Rabeinu Efrayim.
It is worth noting, that while we saw above that the conclusion of the Talmud Yerushalmi (Eruvin 3:9) does not rule like Rebbi Avahu who maintains that outside Eretz Yisrael one holds the Lulav on the first day even though it falls on Shabbos, we can nevertheless learn from the Yerushalmi that everyone agrees that in Eretz Yisrael one holds the Lulav on the first day on Shabbos. This is apparent from the fact that the other Chachamim only disagreed with Rebbi Avahu's teaching to spread this practice to Alexandria, but in Eretz Yisrael itself they agreed with Rebbi Avahu that this is what should be done.
This in fact is written by the Or Same'ach (Hilchos Lulav 7:13). The Or Same'ach writes that this is a dispute between the Bavli and the Yerushalmi. According to the conclusion of the Bavli, even in Eretz Yisrael they never held the Lulav on Shabbos, but according to the Yerushalmi they did.
This is a proof that according to the Talmud Yerushalmi there was no Gezeirah of Rabah in Eretz Yisrael.
1) The Rif Beitzah (3a in Rif pages) writes:
"We learn from here that those who live in Eretz Yisroel are required to observe 2 days of Yomtov on Rosh Hashanah".
We see clearly from the Rif that if one does not keep 2 days of Rosh Hashanah in Eretz Yisroel, one has not done what is required by the Halacha.
2) As we saw above, the calendar was known in advance. The reason that they did not always use the calendar was not because they did not know it, but rather because the Halacha l'Moshe miSinai is that as long as the Sanhedrin exists one determines Rosh Chodesh through testimony, not through the calendar.
We can learn this also from what the Rambam writes in Hilchos Kidush HaChodesh 5:3; that Klal Yisroel only started declaring Rosh Chodesh according to the calculations towards the end of the period of the Sages of the Talmud, because at that time Eretz Yisroel was desolate and there was no fixed Beis Din. However until the time of the later Amoraim, Abaye and Rava, they followed the way that Rosh Chodesh was determined in Eretz Yisroel by the Sanhedrin.
We see from the Rambam that the reason they did Kidush Hachodesh through the witnesses up till the time of Abaye, was because they still possessed a Beis Din, not because they did not know the calcualtions.
3) As we noted before, whilst Rabbi Abahu (Talmud Yerushalmi Eruvin 3:9) told them to take lulav in Alexandria when the first day of Sukos fell on Shabbos, Rebbe and Rebbe Yosi disagreed with him, and since we have 2 against 1, and in addition the 2 opinions against R. Abahu are cited at the end of the Gemara, this suggests that the Halacha does not follow R. Abahu. Indeed the last words in the Sugya in the Yerushalmi is "Do not divert from the custom of your late fathers". This shows us the important of maintaining the minhag, and is similar to what the Gemara Bavli end 4b states (concerning 2 days Yomtov in Chutz LaAretz) "Be careful to follow the custom of your Fathers".
Thank you. Then from this we can clearly infer that the gezeyra deRabba was never intended as a permanent decree by a Sanhedrin, and in fact the gemara never even actually specifies that it was. And obviously the historical reality had to be one or the other in Eretz Yisrael.
1) The Midrash Tanchuma (Parshas Emor #21) states:
"'You shall take the Lulav' even on Shabbos. At the time when the Beis ha'Mikdash stood they used to take the Lulav, but now the later Sages have made a Gezeirah not to take the Lulav on Shabbos lest one go to an expert to learn and carry the Lulav four Amos in Reshus ha'Rabim. The same Gezeirah applies for Shofar and Megilah."
2) The Midrash Sechel Tov Bereshis (Parshas Re'eh, page 67) states:
"Rebbi Zeira said, 'This is a Gezeirah made by the Men of the Great Assembly.'"
3) I do not see any time limit on this Gezeirah. From the Rambam (Hilchos Lulav 7:13-18) it would appear that the Gezeirah is binding until the Beis ha'Mikdash is rebuilt, may it be so speedily in our days.
Let us summarize some of the sources we have for the origin of the "Gezeirah of Rabah."
1) The Gemara (Megilah 5a) writes that Erev Shabbos is the time for reading Megilas Esther. Rashi (DH Erev) writes that Friday is their fixed time from the days of the Anshei Keneses ha'Gedolah. Rashi continues that the Chachamim of Yisrael, after the Keneses ha'Gedolah, instituted that the Megilah reading should be brought forward from Shabbos to Friday because of Rabah.
Rashi does not write that Rabah's is a Gezeirah of the Sanhedrin, but he does write that it is a Takanah of Chochmei Yisrael, and it is not clear if there is any difference between the two terms.
2) Possibly, Rashi is a source for the Midrash Sechel Tov that I cited in my previous reply, that the Gezeirah of Rabah was made by the Anshei Keneses ha'Gedolah.
3) See also the Mishnah at the beginning of the fourth chapter of Rosh Hashanah. The Mishnah states that when Rosh Hashanah falls on Shabbos, the Shofar is blown in the Beis ha'Mikdash. The Tiferes Yisrael (in Boaz) writes that the reason why the Mishnah does not state that on Shabbos the Shofar is blown in Jerusalem (even though, according to the Rambam, one may blow on Shabbos in the whole of Jerusalem) is to teach us that the Gezeirah not to carry the Shofar four Amos in Reshus ha'Rabim is an old Gezeirah that applied even when the Beis ha'Mikdash was in Nov and Giv'on (before the first Beis ha'Mikdash was built in Jerusalem). Back then, they blew only in the city where the Beis ha'Mikdash was, not anywhere else. So the Tiferes Yisrael dates the Gezeirah back to before the first Beis ha'Mikdash.
4) One sees that the Gezeirah of Rabah is a very widespread, ancient Gezeirah. The Gezeirah was made in order to strengthen the observance of Shabbos. It is difficult to imagine how, in our times, when to our great distress the observance of Shabbos is so lax among so many Jews, one would want to change this Gezeirah.
Let us summarize some of the sources we have for the origin of the "Gezera of Rabbah".
1) The Gemara Megilah 5a writes that Erev Shabbos is the time for reading Megilas Esther. Rashi DH Erev writes that Friday is their fixed time from the days of the Anshei Knesses Hagedolah. Rashi continues that the Sages of Yisroel after the Knesses Hagedolah instituted that the Megilah reading should be brought forward from Shabbos to Friday because of Rabbah.
Rashi does not write that Rabbah's is a gezera of the Sanhedrin, but he does write that it is a Takona of Chachmei Yisroel, and it is not clear if there is any difference between the two terms.
2) Possibly Rashi is a source for Midrash Sechel Tov that I cited in my previous reply, that the Gezera of Rabbah was made by the Anshei Knesses Hagedolah.
3) See also the Mishna at the beginning of the 4th chapter of Rosh Hashana. The Mishnah states that when Rosh Hashana falls on Shabbos one blows the Shofar in the Mikdash. Tiferes Yisroel, in Boaz, writes that the reason that the Mishna does not state that on Shabbos one blows in Jerusalem (even though according to the Rambam one may blow on Shabbos in the whole of Jerusalem) is to teach us that the Gezera not to carry the Shofar 4 amos in the street, is an old Gezera that applied even when the Mikdash was in Nov and Givon (before the first Beis Hamikdash was built in Jerusalem). Right back then, they only blew in the city where the Mikdash was, not anywhere else.
So Tiferes Yisroel dates the gezera back to before the 1st Beis Hamikdash.
4) One sees that the gezera of Rabbah is a very widespread, ancient gezera. The gezera was made in order to strengthen the observance of Shabbos. It is difficult to imagine how in our times, when to our great regret the observance of Shabbos is so lax amongst so many Jews, one would want to change this gezera.