We find different practices among the Sepharadiim with regard to the custom to refrain from haircutting (and, for many, shaving) during the Omer period to commemorate the tragic death of Rabbi Akiva's 24,000 students. One practice follows the ruling of the Shulchan Aruch which permits haircutting from the 34th day of the Omer, meaning, the day following Lag Ba'omer. There is some discussion as to whether this position would allow haircutting already during the night after Lag Ba'omer, since in Halacha the new day begins at night, or if the prohibition continues until the morning of the 34th day of the Omer. The rationale underlying the second possibility is that the principle of "Miktzat Ha'yom Ke'kulo," which allows us to consider part of a day equivalent to a complete day, applies only in the daytime hours. Indeed, Halacha generally follows this second view, and thus those who observe the Shulchan Aruch's ruling may take haircuts (and shave, for those who refrain from shaving during the Omer) only from the morning of the 34th day of the Omer. (See Hazon Ovadya, Yom Tob, page 261.)
Children, however, may take haircuts already on the day of Lag Ba'omer. Many follow the custom which is indeed a proper custom to observe to cut a boy's hair for the first time on the third Lag Ba'omer after his birth. Those who follow this custom may cut the child's hair on the third Lag Ba'omer, and need not wait until the next day.
With regard to haircutting for women, the practice among the Sepharadim is to allow women to have their hair cut throughout the Omer period, even before Lag Ba'omer.
The Arizal (Rabbi Yitzchak Luria, Israel, 1534-1572) advanced a much different approach, viewing the entire Omer period as a period of judgment and as a type of "Chol Ha'mo'ed" between the festivals of Pesach and Shavuot. He therefore held that one may not cut his hair or shave throughout the entire Omer period, until Erev Shavuot. Everyone should follow the practice he is accustomed to observing. (See Hazon Ovadya, Yom Tob, page 264.)
As per Hacham BenSion it is permissible to recite the Beracha of She'hecheyanu such as over a new suit during the period of the Omer.
From which point may a wedding be held during the Omer period?
Chacham Ovadia Yosef rules that under extenuating circumstances, such as when the wedding cannot be held on a different day, one may get married on the night after Lag Ba'omer (the night of the 34th day of the Omer). Preferably, however, one should not get married until the night after the 34th of the Omer. This is indeed the Minhag. (See Hazon Ovadya, Yom Tob, page 254.)
Lag Ba'omer is observed as a festive day to celebrate the great contribution of Rabbi Shimon Bar Yochai in authoring the Zohar and thereby making a profound impact upon the world. As such, even though we refrain from haircutting until after Lag Ba'omer, it is permissible to listen to music on Lag Ba'omer (assuming, of course, that the music is appropriate) only in order to celebrate the occasion. Otherwise, music is forbidden until the 34th day.
Summary: Some Sephardim have the practice to refrain from haircutting and shaving throughout the Omer, until Erev Shavuot, while others permit haircutting and shaving on the day following Lag Ba'omer. Women may cut their hair even before Lag Ba'omer, and three-year-old boys may have their first haircut on Lag Ba'omer itself. One may recite She'hecheyanu during the Omer. Weddings should not be held until the day following Lag Ba'omer, though under extenuating circumstances one may get married on the night after Lag Ba'omer. One may listen to music already on Lag Ba'omer only as part of the celebration of this festive day.