O"C Siman 549
Tzom Harevi'i... Regarding the names of our months (Fourth month vs Tammuz) See Rambam Shemos 12:2 - part of the mitzvah of Hachodesh hazeh is to call the months by names which recall yetzias mitzrayim - first, second, third... month to y"m, the first month. (Note how months differ from Shabbos- days of week - rishon, sheni, shlishi... "to Shabbos," which is the seventh day, and months refer back to the first month, most likely because hachodesh hazeh lachem rosh chadashim - it is the "head" of months, but Shabbos, while it is the reference point for the week, doesn't have to be the first.)
(Re beginning of Ramban "ki she'ar mitzvos shebatorah hayu behar sinai." He seems to hold that Hachodesh was not repeated by Moshe to bnei Yisrael at Har Sinai. The Rambam argues on this - see Perush Hamishna, Chulin Perek 7, that Torah is only that which Moshe taught at Har Sinai, so all mitzvos that were given before Har Sinai were given again at Har Sinai.)
(Re end of Ramban - when Bnei Yisrael returned from Bavel they brought the Persian names of the months with them to fulfill the nevua of Yirmiya 16:15 (also see ibid., 23:8). The Rambam does not count the mitzvah to remember Yetzias Mitzrayim every day (by saying the third Perek of Kriyas Shma). Why not? See Hagaddah Siach Hagrid where the Rav brought three answers from Rav Chaim. R' Isser Zalman Meltzer in Even Ha'Ezel (maybe Kriyas Shma 1:3) answers that the mitzvah changes when Mashiach comes, because we will mention the miracles Hashem brought when Mashiach comes which will dwarf the miracles of yetzias mitzrayim. Because the mitzvah will not remain the same after Mashiach comes, it cannot be counted in sefer hamitzvos, because the Rambam only counts mitzvos that are for all time. Now the psukim in Perek 16 and 23 are almost the same, but it seems the Ramban uses [the] one [from Perek 16] to learn there was some commemoration of B"Y leaving galus Bavel, and Rav Isser Zalman uses it [or the one from Perek 23] that while it mentions return from the northern exile, which implies Bavel, really refers to Mashiach.)
Fast of the fourth month. The fast could have been any day within the months of the Pasuk (in Zecharia 8:19), but the dates of the fasts were set. If the fast could have been any day in the month, what if a boy became Bar-Mitzvah during the month, before the fast day (like on the 15th of Tammuz)? The chiyuv of the fast began when the boy was a katan? If that's too extreme to fathom, what about a boy whose bar-mitzvah is on 18 Tammuz in a year when the fast of Tammuz fell on Shabbos and was pushed off to Sunday, the 18th of Tammuz? If the chiyuv to fast is on the 17th, the boy wasn't chayav yet. We pasken that the 13-year old is obligated to fast, but this is something to think about.
Fast of the fourth month. See Rosh Hashana 18b, and Tur & B"Y Siman 550. If there is peace, they fast. Many Rishonim - Tur, Rabbeinu Chananel, many others say peace means the Beis Hamikdash is built. This means in the time of the second Beis Hamikdash, they did not fast, even though the first Beis Hamikdash was destroyed on 9 Av. Rambam (Perush Hamishna R"H 1:3) says in time of the Second Beis Hamikdash they did fast (because they decided to, but they had the right to decide not to fast). I feel we can make a diyuk in the Mishna like the Rambam: it lists 6 months the messengers went out - including Av. The end of the Mishna says in the time of the Mikdash, they'd send out a messenger in another month, Iyar. But the Mishna does not say no messenger was sent for Av. So the fast of 9 Av was observed during the second Beis Hamikdash.
Huchpelu bo tzaros. Tosfos (R"H 18b s.v. Ho'il) asks why is 17 Tammuz different than 9 Av, that on 9 Av we must fast even if there is Shalom but no Gzeiros, but we can choose if we want to fast on 17 Tammuz, but if many bad things happened also on 17 Tammuz we should have to fast? See the two answers of Tosfos. I think the Rambam understands Huchpelu bo tzaros to be discussing the time of the second Beis Hamikdash, 9 Av was already huchpelu - the gzeira in the midbar and the first destruction.