Are sephardim allowed to cut hairs during the three weeks?

Yes, Sephardim are allowed to cut their hair during the three weeks. According to the Sephardic custom, we follow the letter of the law established by the Tanna'im, which prohibits taking haircuts only during the week in which Tisha B'Av falls out, not during the entire three weeks. This is the ruling of the Rambam and Maran HaShulchan Aruch, which we Sephardim follow. The Ashkenazi custom is more stringent - they refrain from taking haircuts from the Seventeenth of Tammuz until the Tenth of Av. However, this is not our minhag. Sephardim may take haircuts throughout the three weeks until the week of Tisha B'Av begins, which starts from the Sunday of that week. If a Sephardi is learning in an Ashkenazi yeshivah or living in close proximity to Ashkenazim, it may be proper to be stringent and follow their custom so as not to look different from one's peers, but this is not a halachic requirement.