While there is always sunrise and sunset in Iceland, from May 19 until July 23 the sun does not set far enough below the horizon for it to be considered night (Tzeis Hakochavim). Therefore the following rulings apply.
1. Maariv may be said from Plag Hamincha, in which case Mincha should be said before Plag Hamincha.
2. Some Halachic authorities maintain that evening Shema may be said from Plag Hamincha. Others maintain that one must say Shema again after Shkiah. According to the Alter Rebbe Shema should be said again after Alos Hashachar (when following the Alter Rebbe's opinion, it is best to say Shema just before Alos Hashachar as well, to be Yotze according to all opinions).
3. You may bring in Shabbos and Yom Tov from Plag Hamincha (including on the first night of Shavuot).
4. On Motzei Shabbos Maariv may be said from Plag Hamincha (including Ata Chonantanu). Havdala may be said from Alos Hashachar. Aish and Besamim should not be used for Havdalah.
5. Kiddush Levana should not be said.
6. Sefiras Ha'omer may be said after Shkiah with a Bracha.
7. Contact Rabbi Feldman or Rebbitzin Feldman regarding using the Mikvah.
Reykjavik does not have an Eiruv.
Please contact Rabbi Feldman for further questions.