What is "Tzom ha'Revi'i"?
Rashi: The fast of Tamuz, which is the fourth month. Radak - it is the 17th of Tamuz, on which the city was breached 1 .
Yirmeyahu 39:2: The breach was in the ninth [in Churban Bayis Rishon]. Refer to Yirmeyahu 39:2:1:2 and the note there. (PF)
What is "Tzom ha'Chamishi"?
Rashi: The fast of [Radak - Tish'ah b']Av.
What is "Tzom ha'Shevi'i"?
Rashi: The third of Tishrei, on which Gedalyah as killed.
What is "v'Tzom ha'Asiri"?
Rashi: The fast of Teves. Radak - it is the 10th of Teves, when Melech Bavel besieged Yerushalayim.
Why does it say "l'Veis Yehudah"?
Radak: This discusses Bayis Sheni; the 10 tribes did not return.
What do we learn from "veha'Emes veha'Shalom Ehavu"?
Yevamos 14b: Even though Beis Shamai and Beis Hillel argued about laws of Yibum and other matters that affect Kidushin, Beis Shamai did not refrain from marrying women of Beis Hillel, and vice-versa.
Radak, Malbim: You will not fast these four fasts, on condition that you love Emes and Shalom, like I commanded you.