Gedaliah was killed on Rosh Hashanah. We fast the day after Rosh Hashanah, so as not to fast on Yom Tov. (Radak)

See Shulchan Aruch, section 559, Mishnah Brurah, item 2, about why we fast to commemorate the death of Gedaliah.

Yishmael was from the house of David, and was jealous that Gedaliah, and not he, had been appointed as the new leader. (Radak)

All the men struck Gedaliah, but it ws Yishmael who killed him. (Metzudat David)

Gedaliah was killed because of the jealousy created by his new position. (Metzudat David)

He killed only the men of war - the rest he took captive. (Metzudat David)

This is mentioned in connection with the next verse. (Metzudat David)

The murder was not yet publicized. (Metzudat David)

They were in mourning over the destruction of the Temple and the exile of Yehudah. (Metzudat David)

Even though there was no Temple, they were still able to bring sacrifices. (Metzudat David)

Note: One may do this only if the exact spot of the altar is known.

He pretended to cry over the destruction of Jerusalem, in order to deceive them. (Metzudat David)

Instead of letting them go to Jerusalem, he took them to the Mitzpah, where he would be able to kill them more easily. (Metzudat David)

He did not want them to hear about Gedaliah's death, because they might try to avenge him. (Metzudat David)

See Melachim I 15:16-17. Baasha wanted to prevent the people from going up to Jerusalem three times a year for the holidays (aliyah laregel). Asa tried to remove the threat of Baasha. This pit represented their struggle. It is mentioned here in order to note one of the primal causes of the downfall of the Jewish kingdoms. (Da'at Sofrim)

1. In the place of Gedaliah in the Mitzpah. (Metzudat David)

He took captive those who had fled and returned to the land of Israel. (Malbim)

Those being taken into captivity. (Metzudat David)

The people turned from Yishmael and joined up with Yochanan. (Metzudat David)

In the place where Kimham had lived. See Shmuel II 19, 38-39. Kimham was the son of Barzilai, and he ate at the table of King David because of the kindness his father had shown to the king. (Metzudat David)

They were afraid that the Babylonians would think that the entire nation was behind the conspiracy to kill Gedaliah - the assassination of an officer of the king is a sign of rebellion against the king. (Metzudat David)