From an Ashkenazi perspective, Kitzur Shulchan Aruch 122:6 writes both customs exist
On the three Shabbosos between the seventeenth of Tammuz and Tishah
beAv, we read the "Three haftaros of retribution," which are: [...]
Shim'u devar Hashem, (Hear the word of Hashem) (Jeremiah 2:4) [...] If
Rosh Chodesh Av occurs on Shabbos, he reads the haftarah [normally
read on Rosh Hodesh] Hashamayim Kis'i (The heaven is My throne)
(Isaiah 66), but in some communities, the haftarah Shim'u is read.
Rema (SA OC 425:1) mentions both customs, Shim'u (Abudharam, Mordekhi) v' yesh omrim Hashamayim Kis'i.
Artscroll's humash has Shim'u devar Hashem while noting "some congregations read the Haftara for Rosh Hodesh". Koren's humash and Tanakh give Shim'u devar Hashem for parasha Masei without noting a different haftara for Shabbat Rosh Hodesh.
I also consulted the "luach dinim u'minagim kminhag edot Israel" (see p. 76) from Heichal Shlomo which is the standard calendar used by national religious synagogues in Israel. It has Shim'u devar Hashem as the haftara but adds that some also say the first and last verse of the Rosh Hodesh haftara.
I found (in R Chaim Drukman's book Step by step) one possible reason that might explain why we should read a "haftara of punishment" even if Rosh Hodesh falls on Shabbat. Abudraham (here) writes the sequence of the seven Haftarot of consolation is a running conversation between God, the prophets and Knesset Israel. As such one should not "interrupt the conversation" by reading haftara Rosh Hodesh in the middle. Possibly the same idea applies to the haftarot before 9 Av.
On your last question re R Huna, Artscroll's gemara Megila 31b notes that "we" do not follow the Gemara in this instance, as we follow the opinion to start the heavier mourning for 9 Av during the week that it falls in and not (as in Rav Huna's view) from Rosh Hodesh Av. As such we do not read Isaiah 1:14 on Rosh Hodesh Av but on the Shabbat immediately preceding 9 Av.