What did Yo'av hear?
Rashi: He heard David's command to kill him, and he knew that Shlomo hates him.
Radak: He heard that Adoniyahu was killed and Evyasar was expelled.
Why does it say that Yo'av did not veer after Avshalom?
Rashi citing Sanhedrin 49a: He thought to support Avshalom. He did not, for David still had some of his strength. 1
Radak: Had he veered after Avshalom, but not after Adoniyahu, he would not fear. Since all of Yisrael wanted to make Avshalom king, this is not a rebellion for which one is Chayav Misah. If we would not say so, Amasa was Chayav Misah. David wanted to make him the head general, and considered Yo'av liable for killing him! Yo'av was liable for this rebellion, for he knew that David wanted to make Shlomo king; he rebelled against David and Shlomo.
Radak citing Ibn Ezra: He did not veer after Avshalom, for he thought that Avshalom is not proper for kingship 2 ; he thought the same about Shlomo.
Malbim: Had he veered also after Avshalom, this would show that he thinks that kingship goes to the oldest; if so, he would not be Chayav Misah now, for he thinks that Adoniyahu should be king. However, Yo'av did not support Avshalom - he killed him! Rather, Yo'av supported Adoniyahu amidst fear lest Shlomo kill him for killing Amasa.
This is like R. Elazar. R. Yosi b'Rebbi Chanina says that he did not, for David's strong-arms were still around.
Perhaps Yo'av saw Avshalom bestows bad to those who help him. Yo'av schemed via the Ishah Chachamah to get David to return Avshalom, and Avshalom told his servants to burn Yo'av's field (Shmuel II, 14:30)! (PF)
Why did Yo'av grab onto the corners of the Mizbe'ach?
Radak (29, citing Chazal): He erred 1 about Kelitah (refuge) of the Mizbe'ach. It is Kolet only Shogeg, and only the roof of the Mizbe'ach is Kolet 2 (and he grabbed the corners). Malbim citing Makos 12a - also, it is Kolet only a Kohen engaging in Avodah, and he was a Zar. Also, only the Mizbe'ach in the Mikdash is Kolet; he went to Ohel Hashem.
Radak (30): He wanted Shlomo to be punished for killing him on the Mizbe'ach.
Radak (30, citing Chachamim, Sanhedrin 48b, and Malbim citing Yerushalmi Makos 2:6): He did not want to be killed via Shlomo [for Mored b'Malchus], for then his property would go to Shlomo [and not to Yo'av's heirs].
Radak (30, Radak citing R. Yehudah, Sanhedrin 48b): In any case his heirs would inherit his property. He refused in order to live a small additional time (until Shlomo would hear and command to take him).
Radak (30) and Malbim (30, citing Bamidbar Rabah 23:13): He wanted to be killed via the king, for then he is buried in his ancestors' gravesite. Those killed by Beis Din are burned in a cemetery of Beis Din. :
Radak citing Tanchuma Mas'ei 12: Yo'av was Rosh Sanhedrin - "Yoshev ba'Sheves Tachkemoni" (Shmuel II, 23:8). He would not err about this! Refer to 2:28:3:2.
Radak: We expound "me'Im Mizbechi" (Shemos 21:14), but not me'Al Mizbechi. (Radak, Bamidbar Rabah 23:13 and Tanchuma Mas'ei 12 connote that there is no refuge at all for Mezid. The verse discusses Mezid - "v'Chi Yazid", and we expound that if he is in the middle of Avodah, he finishes it before we take him to execute him! However, one can explain Radak and the Midrashim to say that it is a mistake to think that the Mizbe'ach shelters one who is Mezid, i.e. a Zar who cannot serve on it; they agree that a Kohen, even Mezid, finishes the Avodah before he is taken. Bartenura (Shemos 21:14, citing the Gemara) says that there is no refuge at all for Mezid (also Ibn Ezra says so, but he concedes that Chachamim expounded unlike this); our text in Sanhedrin 48b said so only about Arei Miklat, and that the Sar of Edom erred about this. It also says that Yo'av thought that he was permitted to kill Avner (he was Go'el ha'Dam) and Amasa (he was Mored b'Malchus)! (PF)
Why did Yo'av grab onto the Mizbe'ach only now?
Radak: Before he was not afraid due to his rebellion, for Shlomo pardoned Adoniyahu, who rebelled, and those who helped him. When he heard that Shlomo killed and expelled Evyasar, he was afraid for himself.
Where was the Mizbe'ach?
Radak: It was in Ohel Hashem, where the Aron was. There was a Mizbe'ach there; David had offered Olos and Shelamim in front of the Aron (Shmuel II, 6:17).
