2. Question: Why did Rabbeinu Tam just walk up to the bima for the third aliyah even though he was not called up for it on Shabbos when he was in the middle of shiva?
A. Learning Torah is one of the things forbidden to be done while mourning during shiva.
B. On Shabbos private mourning is observed, like no Torah learning.
C. Torah reading at minyan is considered learning Torah, hence a mourner should not get an aliya during shiva.
D. Rabbeinu Tam used to get the third aliyah every Shabbos.
Answer: To not get an aliyah for Rabbeinu Tam would be observance of public mourning since he normally got one every Shabbos so he just went up on his own though the gabbai did not call him up so that he would not be publicly mourning on Shabbos which transgresses the honor of Shabbos. (See Yoreh Deah 400:1and the Rema says that for this reason if there are no other kohanim the mourner should be called up for the aliyah and also the Pischei Teshuva Yoreh Deah 399:1 says that a mourner can get an aliyah on Simchas Torah when every single person gets an aliyah for the same reason, that if he doesn’t then it will be obvious that he is in mourning and it will become public mourning which can’t be done on yom tov.)