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 [...
The mishna berura writes in hilchos tefilin siman 36 in the name of the kneses hagedola that a person should follow every area of the kabola/zohar that is not in contradiction to halocha. but it is not obligatory
The Midwest Agudas Yisroel Council of Synagogue Rabbonim writes here, p. 32, that the restrictions of 10 Av midday extend to wearing freshly laundered clothing
The following is a list of the activities that remain forbidden until
chatzos on the 10th of Av and the possible exceptions
Eating meat and drinking wine (Food cooked with meat is permissible).
One of the earliest sources of an oath or vow, we find in Bereishis 8:21 that Hashem swears never to bring another flood (see Rashi, based on Shevuos 36a).
For a case of a vow of restraint being taken and then being annulled. The Kli Yakar Bereishis 8:16 Noach forbade himself from yichud and when Hashem told him he may have relations it was annulled.
We see that from the very beginning the avos would utter a neder or a shevua. The earliest reference to a shevuah is in Lech Lecha 14:22
22 And Abram said to the king of Sodom, "I raise my hand to the Lord,
the Most High God, Who possesses heaven and earth.
I raise my hand: Heb. הֲרִימֹתִי, lit. I raised. This is an expression
of an ...