Rashi: Shevi'i is Tzom Gedalyah. Radak - the Churban was in Chamishi. Gedalyah was killed in Shevi'i. This was like a second Churban. Until his death, there was a remnant of Aniyim that Nevuzaradan left in the land for Chormim v'Yogvim. Gedalyah was killed on Rosh Hashanah. Since it was Yom Tov, the fast was fixed on the day after Yom Tov.

Rashi: There is Chataf Patach under the Hei, for this is said in astonishment. Did you fast for My honor, that also now you must fast?!

Radak: Did you fast due to Me? The Churban and Galus were due to your sins. This is why you fasted. If you will do Mishpat and Tzedakah, you need not fast, for the Bayis will be built, [everyone] will ascend from Galus and dwell in the land forever, if you will do good in My eyes. You will never be exiled from it. It adds "Ani" - did I command you to fast?

Malbim: Man must resemble Hashem's ways, to do Chesed, Mishpat and Tzedakah. Then, Hashem is aroused to conduct with him will these Midos. This is only in matters used to describe Hashem, e.g. Rachum, Chanun, Tov and Salach. If man fasts and afflicts his Nefesh, how will Hashem be aroused correspondingly? Eating and drinking do not apply to Him! Our verse says, if you will fast, will this cause Me to fast?!