Rabbi Zalman Baruch Melamed was asked onwebsite why these two special days are connected. Aren't they contradictory?
He answered that the establishment of the state is dependent on the people who sacrificed themselves on the altar of klal Yisrael so we should have the privilege to live in the land of Israel. By linking these two days we express the recognition that we know that thanks to them, the state was born and continues to exist.
Rabbi Ari Shvat was asked on the site why we celebrate the new festival of Yom Haatzmaut. Pausing the laws of mourning, and instigating hallel seems a bit too much for what seems to be only a very very minor festival.
Rabbi Shvat gave a long and comprehensive answer to explain the importance of this special Independence Day. The return of the nation of Israel to its land and the building of a state is a big Kidush Hashem especially when coming so close after the holocaust. The state has been a place of refuge since its establishment for millions of Jews who were haunted in the countries of the diaspora. Also since the nation of Israel declared independence we came back to fulfilling lots of Mitzvot that we couldn't fullfill in the diaspora. To read the Full answer.
One of the yeshiva.co surfers asked if one should say Hallel on Yom Ha'Atzmaut and can one take a hair-cut even though we are in the mid of the counting of the Omer? Rabbi Roi Margalit gave him the answer that there are different Minhagim regarding the reciting of Hallel. As to the hair-cut Rabbi Margalit answered that the Cheif Rabbinate of Israel instructed that this day is a day of gratitude for the big step of redemption we experienced, but there are several opinions on taking a hair-cut. The mostly accepted opinion is that hair-cuts and shaving are allowed on Yom Ha'Atzmaut.
To engage further Shiurim or Q&A regarding Yom Ha'Atzmaut and Yom HaZikaron.