If I observe the ’omer restrictions after Rosh Chodesh Iyyar and trim my beard ’erev Shabbat, can I shave and/or get my hair cut on the following days? Yom Ha’atzmaut? Lag Ba’omer? Yom Yerushalayim? Rosh Chodesh Sivan?

Shalom, Thank you for your question. As you know there are different customs as to when we refrain from haircuts during the Omer period. According to your custom to start the restrictions from Rosh Hodesh Iyar, you may get a haircut as follows – 1) Many great rabbis in the religious Zionist world rule that one may get a haircut in honor of Israel Independence day. That is even on the afternoon before the Yom HaAztamaut. If you have unkempt hair that looks like it is a "mourners" length, you should certainly get a haircut in honor of day, so as not to appear in mourning on a festive day. 2) Lag B'Omer – the Ashkanazi tradition is to allow haircuts during the daytime of the 33rd day. When Lag Ba'Omer falls on a Sunday, as it does this year, it is permissible to get a haircut on Friday day. 3) Again, there are rabbis who allow getting a haircut and shaving in honor of Yom Yerushalim. 4) In relation to Rosh Hodesh Sivan – there are different customs. The Mishna Brurah (493,3, Mishna Brurah 15) writes that those who began not shaving on Rosh Hodesh Iyar may not start again until Shavu'ot (that is, on the day before the Festival) [except for Lag Ba'Omer, as above]. He then writes that the custom is to allow haircuts during the "three days of restriction" i.e. the morning of the 3rd of Sivan. He then quotes a third custom that allowed haircuts from Rosh Hodesh Sivan already (– though in the Sha'ar HaZion there he questions the source for this leniency). So, as you see, the majority of opinions do not allow a haircut on Rosh Hodesh Sivan, for those who started from Rosh Hodesh Iyar – those who started refraining from haircuts from the start of the Omer generally allow haircut from Lag B'Omer onwards. If you do not have a family or community tradition, you should wait until the 3rd of Sivan, or erev Shavu'ot to get a haircut. Blessings.