How can the two noble verses {And We made the night a covering, and We made the day for livelihood} and {Eat and drink until the white thread becomes distinct to you from the black thread} be reconciled with regions where the day or night is exceptionally long?

Islam is a religion for all. The verse: "And We made the night a covering. And We made the day for livelihood" indicates Allah's favor upon His servants by making the night for rest and the day for striving. Depriving some people of this is to show Allah's power. Sharia rulings are based on the general case, and exceptions have their own specific rulings. As for the verse: "And eat and drink until the white thread of dawn becomes distinct to you from the black thread [of night]," in countries where night and day are not distinguishable, estimation must be made based on the nearest country where night and day are distinguishable, by analogy with the hadith about the Dajjal in Sahih Muslim.