3. When does the fast end?
All fasts conclude after nightfall. This is defined as the sighting of three medium stars, or when the moon shines very brightly on the earth. It however does not suffice to see three large stars. [Practically, in Eretz Yisrael, some say that this is approximately 17 minutes after sunset by regular fasts and 24-27 minutes after sunset by Tisha B’av. Others say it is 27 minutes after sunset by all fasts of the winter, and 34-35 minutes after sunset by all fasts of the summer. According to the rulings of Rav Avraham Chaim Naah, nightfall in Eretz Yisrael is between 15-20 minutes after sunset in the winter and 20-26 minutes after sunset in the summer. In New York, some write one is to wait until 50 minutes after sunset, or at the very least 41 minutes after sunset. The Rebbe stated that in New York nightfall throughout the year is 36 minutes after sunset, both during the summer and winter. In all cases, one may begin Maariv before the above time, in order to conclude Maariv and be able to eat when the above time arrives. In such a case, one is to make sure to read Kerias Shema again after nightfall.]
If one is flying on a fast day and is extending or hastening the sunset, when is he to break his fast?
He is to break his fast as soon as Tzeis Hakochavim arrives in the area that he is currently in. Thus, if he flew from the U.S. to Israel and is hence hastening the coming of Tzeis Hakochavim, he may to break his fast as soon as Tzeis Hakochavim arrives on his plane. If, however, he flew from Israel to the U.S. and is hence delaying the time of Tzeis Hakochavim, then he is to fast until Tzeis Hakochavim arrives while he is on the plane. Some Poskim however rule that when flying to the west, one may be lenient to break his fast in accordance to the area that he left from, upon Tzeis Hakochavim arriving there.
When does the fast end in countries with long days, such as near the North pole?
If one crossed the international dateline on a fast day from West to East, is he to fast again the next day?
 Michaber 562:1; See Piskeiy Teshuvos 562:1
 Michaber 562:1; Rosh; Rav Chisda in Taanis 12 “Whoever did not fast until sunset is not considered to have fasted.” Igros Moshe 4:10 rules that in New York one is to wait until 50 minutes after sunset, and at the very least wait 41 minutes.
Other opinions: Some Poskim rule it one is only required to fast until the start of Bein Hashmashos. [Sefas Emes Taanis 12; Aruch Hashulchan 562:9 based on Rambam, Rashi, Ran] This however is in reference to Zman Rabbienu Tam, and not to the Zman of the Geonim. [Biur Halacha Tinyana 562; Piskeiy Teshuvos 562:1]
 Rama ibid; Hagahos Ashri; Hagahos Maimanis
 M”A 562:1 as corrected by Machatzis Hashekel ibid; Levushei Serud ibid; P”M 562 A”A 2
 Luach Eretz Yisrael of Harav Tukichinsky
 Sefer Birur Halacha, brought in Piskeiy Teshuvos 562:1
 See Ketzos Hashulchan 93 footnote 2; Shiureiy Tziyon of Grach Naah p. 76
 Igros Moshe 4:62; See Rebbe in Igros Kodesh 17:124 [printed in Shaareiy Halacha Uminhag 155 and Shulchan Menachem 2:123]
 Heard from Rabbi Leibal Groner; See Hiskashrus 370:19; Rav Raskin in Siddur p. 230
 Mateh Efraim 602:29; Igros Moshe ibid; Piskeiy Teshuvos 562:1 footnote 2; Rabbi Groner that so was directive of Rebbe to ask Rav Shmuel Levitan one year on a fast day to Daven before the time of nightfall and announce to everyone to say Shema again after nightfall; See Hiskashrus 1198
 Igros Moshe 3:96; Betzeil Hachochmah 1:31; Chavatzeles Hasharon 1:43; Yaskil Avdi 8:31; Piskeiy Teshuvos 562:2; See Nitei Gavriel Bein Hametzarim 4:5
The reason: As there is no precedence in Poskim to allow one to break one’s fast based on the area that he started his fast, and hence since the law states that the fast does not end until Tzeis Hakochavim, one may break the fast when it reaches Tzeis Hakochavim in his area, whetehr this is earlier, or later, than his original location. [Igros Moshe ibid]
 Shevet Halevi 8:261; See Nitei Gavriel ibid
 The reason: A the Sages never decreed for one to fast more than the normal hours, and hence one may break his fast as soon as the fast is over in his original location. [ibid]
 See Piskeiy Teshuvos 562:2
 Nachal Eshkol Tisha B’av
 Daas Torah 549; Shevet Halevi 7:76
 Betzeil Hachochma 1:31