1. The gemara in 22a has a discussion on the number of aliyot in a taanit.
Usual question - what did they did every taanit?
Here they try and learn from a story about Rav. Why not do what their
rebbe did in the yeshiva?
2. in 29b there is an argument over what we layn for shekalim.
The gemara asks a question from the haftora. How come the layning is
in dispute but the haftora everyone agrees on. Why not just say that there
is also a dispute about the haftora?
3. on 27b the gemara asks why R. Elizer ben Shanua lived a long life.
According to ele ezkara on yom kippur he was one of the 10 marytrs.
He is also listed as a student of Rav Akiva and got semicha from Rav Yehuda ben Bava.
Hence, it is unlikely he lived longer than Rav yehuda or Rav Yose etc.4. You mention in the insights on 26a that Shilo, Nov & Jerusalem were in the section of Binyamin. According to my maps shilo is in Ephraim and I recall seeing that written somewhere, but didn't have a chance to look it up.
1. There were various practices that had developed, and they were inquiring
which one is the correct practice. They decided to learn from a story about
Rav, because Rav was the leader of the Jewish people, considered like a Tana,
and none of the Amora'im could argue with him (see Tosfos in Beitzah 9a, DH
v'ha'Amar).
2. The Haftarah ("Yehoyada ha'Kohen") is explicitly mentioned in the Beraisa,
but the what Keri'ah is itself is not mentioned in the Beraisa or discussed
by the Tana'im. Hence, the Amora'im argue what the Keri'ah is.
3. The Asarah Harugei Malchus were killed at different times. The first three
were killed on 25 Sivan 3828 (see Shulchan Aruch OC 580), and the remaining
seven were killed in 3880 (among them were R. Akiva and R. Yehudah b. Bava).
(From TZEMACH DAVID, cited by the SIFSEI CHACHAMIM in his introduction to
Maseches Rosh Hashanah; see also Eisenstein on "Midrash Asarah Harugei
Malchus" and others.)
4. The Gemara in Zevachim (118b) asks this question and answers that the city Shilo was in the Chelek of Binyamin, which contained the Shechinah in Shilo, and there was a strip of land that of the Chelek of Yosef (Efraim) which contained the Sanhedrin of Shilo (see the Gemara there, which concludes that it is a Machlokes Tana'im whether the Shechinah dwelled in the Chelek of Binyamin in Shilo; perhaps this question is the reason why Rashi does not explain like the Torah Temimah which we quoted in the Insights).
Kol tuv,
Mordecai