I’m not certain of the halachic status of Eilat, but as for your second question…how in the world can an eruv affect the seven-day or eight-day Passover holiday? An eruv just allows carrying on the Sabbath in that area. Passover is still eight days outside of Eretz Yisrael, whether in Ann Arbor or anywhere else.
But if you consider yourself a resident of Eretz Yisrael, you only need keep seven days…but you’re supposed to keep any eighth-day activity low-key.
I didn’t know that anyone who follows halacha actually lives in Eilat. Wow, I guess you do learn a lot on the SDMB.
IMHO (not that it matters anymore for this year), your question really exemplifies where the rubber meets the road on the political vs. the religious significance of the modern state of Israel. There are some halachicly observant jews who do not recognize the modern state because, in their opinion, it was not brought about by Mashiach. For them, Eilat would be diaspora.
If, however, you recognize the modern state and support it in its continued existence (as well as its continued struggle for peaceful borders), then to consider Eilat a part of the diaspora would, in effect, give up any “claim” that the modern state might have to any land which might be outside of Eretz Yisrael. In addition, using only the biblical borders would make compromise virtually impossible in the current struggle
IMHO, to discount the modern state’s borders in your halachic practices would be short-sighted considering that Medinat Yisrael can use all the help she can get right now. I would hate to think that those working to shrink the modern state’s borders would use the eighth day of Pesach against the Israeli government’s position in certain areas.
As far as I know, a resident of Eilat should keep 7 days of Pesach, not 8. But this is a question for you LOR (locally ordained rabbi),especially if it is relevant specific to your situation. But how many days an individual keeps is not based on where a person is located, but on where a person resides. (In other words, and American in Eilat, or Jerusalem for that matter, would keep 8 days. An Israeli in Beijing or Moscow or anywhere would keep 7 days.)
And Michigan is certainly outside of Israel, though the Arab population in the state, particularly around Detroit, might make it seem a little like the Middle East…