Is it permissible to cut hair on Rosh Hodesh Av when it comes out on a Friday?
One should not take a haircut on Rosh Chodesh, even if it comes out on Friday and the haircut will be taken in honor of the Shabbat.
Yechaveh Daas 4:36 says that one may take a haircut on Rosh Chodesh Av, on whichever day of the week it occurs.
Last week, I asked a respected individual learned in Torah in my community when (in July 2012) it would be forbidden to shave and get haircuts. The answer I received was from the 22nd until the 30th. This answer seems to imply that he would permit shaving and haircuts on the upcoming Rosh Hodesh this Friday.