Gemoroh answers that Rabban Gamliel wrote those letters after he was deposed. This implies that the reference is to Rabban Gamliel from Yavneh who was Nossi after the destruction of the Temple. If this is the case then:
1) What was he doing with his scribe writing letters on Har haBayis?
2) What is the meaning of "the time of Biur has come"?
According to many Rishonim there was no Biur Maaser after the destruction of the Temple (see Minchas Chinuch #607).
3) What is the relevance of "birds are young and sheep are tender" since there were no sacrifices then?
Michael Dalezman, Brooklyn,NY,USA
Chamra v'Chayei brings from She'eilas Ya'avetz that Yavneh was in Galil, and therefore Raban Gamliel had to come to Yehudah to make Ibur Shanah. She'eilas Ya'avetz also writes that there are those who wish to prove that Korbenos Tzibur were brought after Churban ha'Bayis from the words "the sheep are tender." However this will not explain the expression "birds are young." It is therefore more likely that this was simply a standard text that was used for Ibur, see Margaliyos Hayam.
Chamra v'Chayei himself disagrees and suggests that the Gemara is indeed referring to Raban Gamliel the first.
Tzuntz, in his yearly periodical (some 70 years ago) brings those who tried to prove from the lines "the sheep are tender and the brids are young" that Bar Kochba rebuilt the Beis ha'Mikdash and offered Korbanos after the Churban. In the next edition (in an article entitled "Churban ha'Bayis ha'Shelishi") another author rejected the claim. Archaeology supplies convincing support for the second article; among the tens of thousands of coins found in digs in Yerushalayim, but a single coin minted by Bar Kochba was found. The statement about birds and sheep must have been a standard text that was used, despite the fact that Korbanos were no longer offered.
As for the Har ha'Bayis, the Chachamim may have been in Yerushalayim for a mission of some sort when the made the Ibur. (Although Yerushalayim was off limits to Jews at one point, that was only after the Bar Kochba revolt, see end of Makos).
As for Bi'ur Ma'asros, it is important to note the distinction between Bi'ur and *Viduy* Ma'asros. There was no Viduy, but there still was Bi'ur. See Rambam.
See also Margoliyos ha'Yam, who suggests that they used the terminology that was used in the times of the Mikdash since every day we await its rebuilding. This is also tied in to what the Gemara teaches in Sukah 41a, "Avdinan Zecher l'Mikdash."
1, 3) Regarding questions 1 and 3, see Maharatz Chayos who basically asks these two questions on the view of Rashi and Tosfos -- that we are talking here of Raban Gamliel of Yavneh.
He answers according to Tosfos Rabeinu Peretz that "Basar d'Ibruha" does not refer to the deposing of Raban Gamliel, but to the intercalation of the leap month. Hence, it could be talking here about Raban Gamliel ha'Zaken.
There is, in any event, much discussion about when the Gemara is referring to which Raban Gamliel. See Nidah 6b, Tosfos DH b'Shifchaso (Machlokes Rashbam and Tosfos), and Maharatz Chayos and Rashash there. See Pesachim 74a and Rashash there. See also Sanhedrin 11a and Aruch la'Ner there (DH Shimon v'Yishmael).
Regarding our Gemara (11b), Rashi and Tosfos clearly relate it to Raban Gamliel of Yavneh, so the question remains. It is in fact to be found asked in the Chidushei ha'Ran: "And this is difficult, because after the Churban how could they be sending letters saying that 'Gozlaya Rechichin...'? It must be that even after the Churban, they would look into those things which would be necessary if the Beis ha'Mikdash would be standing, so that if the Beis ha'Mikdash is rebuilt in their days, everything will be ready..." (see there).
See also Toldos Tana'im v'Amora'im, Erech "Raban Gamliel ha'Zaken," pp. 306-307, who seems to have come to the same conclusion without having seen the Ran. (Photocopy attached.)
I did in fact write about this subject from a different perspective in Ha'Meir, Yisro 5751 (in rebuttal of the proofs of the Maharatz Chayos that the Korban Pesach was offered even after the Churban). A copy of the relevant parts is also attached.
2) Regarding the second question, it seems that the question is based on a misunderstanding. Bi'ur Ma'asros -- which still applies today -- should not be confused with Viduy Ma'asros, which does not apply today according to most opinions. (This in fact is apparent from the Minchas Chinuch #607 quoted in the question.) See Kitzur Dinei ha'Mitzvos ha'Teluyos ba'Aretz 12:6 (based on the rulings of the Chazon Ish): "According to most authorities, the obligation of Viduy Ma'asros applies only in the times of the Beis ha'Mikdash" (see there for the reason). Bi'ur, however, still applies today in full force, at least mid'Rabanan.