If one says Hallel on Yom Haatzmaut, when does one say it when they change the holiday away from 5 Iyar because of Shabbat or other reasons? Does one say it on 5 Iyar or on the day the holiday is celebrated? can one still say it with a Bracha if one follows that Minhag?

One should observe Yom Haatzmaut on the day that is determined by the State of Israel in consultation with the Chief Rabbinate. All the laws and customs of Yom Haatzmaut should be observed.