Asking a Kohen to leave the Shul-In a time of need, may one forgo the Aliyos of a Kohen and Levi and give it to a Yisrael?
Some Poskim rule that the Sages instituted that a Kohen and Levi cannot forgo their honor and allow a Yisrael to be called up in their place. Thus, Mechila does not help to allow a Yisrael to be called up first or second. Accordingly, some Poskim rule that it is forbidden to ask a Kohen to forgive his honor and leave the Shul in order to call up a Yisrael in his place even if one desires to sell the Aliyos, or call up guests or Chiyuvim. Other Poskim, however, rule that a Kohen or Levi may forgo their honor and have a Yisrael called up in their place. Accordingly, some Poskim rule that in rare mitigating circumstances [i.e. special opportunity to sell Aliyah for much money; many guests; many Chiyuvim], it is permitted ask the Kohen to forgive his Aliyah in order to call up a Yisrael in his place. In such a case, some Poskim rule that the Kohen is to leave the Shul prior to the start of the Aliyah. Other Poskim, however, rule that it is not necessary for him to leave the Shul, and thus in such a case the Gabaiy is to say Bereshus Hakohen. [Practically, the custom is like the former opinion. Nonetheless, in a time of need, the custom is to ask the Kohen to forgive his Aliyah and to leave the Shul in order to call up a Yisrael in his place. Even according to the above opinions, it is forbidden to make a set standard of not calling up the Kohen and it may only be done in the enumerated mitigating circumstances.]
The Chabad custom: The Chabad custom is to be very particular in the order of the Aliyos and to endeavor to always arrange for a Kohen, and then Levi, and then Yisrael to be called up. [Nevertheless, on rare occasions, such as to give two Bar Mitzvah boys an Aliyah on a Monday or Thursday, one may ask the Kohen to forgive his Aliyah and leave the Shul.]
In a time rare and mitigating circumstances [i.e. special opportunity to sell Aliyah for much money; many guests; many Chiyuvim] the custom is to ask the Kohen to leave the Shul in order to call up a Yisrael in his place.
If a Yisrael was intentionally called up in place of a Kohen despite him not forgiving his honor, is one Yotzei the Aliyah?
Some Poskim rule that in such a case the Aliyah of the Yisrael is invalid and hence the Kohen must be called up again and repeat from that Aliyah.
 See Piskeiy Teshuvos 135:9
 Levush 135; M”B 135:9; Kaf Hachaim 135:12; Rav Amram Gaon; Rav Nutranaiy Gaon, brought in Tur 135; See 2nd opinion in Admur 128:60
 Shivas Tziyon 6:6; Lev Chaim 93 in name of Batei Kehuna; Avnei Tzedek 9; Daas Sofer 1:18 in name of Chasam Sofer; Zichros Yehuda 74; Maharshag 1:44; Levushei Mordechai 6; M”B 135:18
 Admur 128:60 in parentheses “As a Kohen may give permission to a Yisrael to be called first and say the blessings before him, as written in 135 and 201”; Tur 135 in name of Rosh Gittin 5:20 that it is permitted to do so on Mondays and Thursdays; M”A 201:4 in name of Semag
 M”A 135:7 and Maharik Shoresh 9 regarding custom of some communities to sell Aliyah of Kohen to highest bidder, brought in M”B 135:18 [However the M”B explains this to be an exceptional case being that it is an old custom, and done for Kavod Hatorah]; Teshuvah Meahava 1:91; Kesav Sofer 36; Shnos Chaim p. 86; Shoel Umeishiv Shetisa 29; Maharam Shick 60; Maharsham 1:214; Toras Chaim Sofer 135:7; Igros Moshe 2:34; 3:20; Minchas Yitzchak 2:41; Shevet Halevi 8:25; Teshuvos Vehanhagos 1:151; Yabia Omer 6:23; Mishneh Halachos 3:13; Tehilos David 40
 M”A 135:7; Maharik Shoresh 9; Chasam Sofer 24-25; Teshuvah Meahava 1:91; Kesav Sofer 36; Shoel Umeishiv Shetisa 29; Maharam Shick 60; Maharsham 1:214; Toras Chaim Sofer 135:7; Igros Moshe 2:34; 3:20 regarding Shabbos and Yom Tov; Minchas Yitzchak 2:41; Shevet Halevi 8:25; Teshuvos Vehanhagos 1:151; Mishneh Halachos 3:13
 Beis Yosef 135; Peri Chadash 135:3; Kneses Hagedola 135; Emes Leyaakov 46; Ledavid Emes 5:46; Birkeiy Yosef 135:8; Maharash Kluger in end of Sefer Stam; Eretz Chaim 135; M”B 135:18 regarding Shabbos Bereishis; Shnos Chaim p. 86; Kaf Hachaim 135:14; Igros Moshe 2:34; 3:20 regarding weekday readings; Yabia Omer 6:23; Tehilos David 40; See Sichat Hashavua Pinat Halacha 459
 As rules Michaber 135:4
 Sefer Haminhagim p. 30 [English]; Likkutei Dibburim Likkut 13:5 vol. 2:311; Sefer Hasichos 5696 p. 51
 See Sichat Hashavua Pinat Halacha 459 that so was once done by the Rebbe
 Arugas Habosem O.C. 21; Zecher Yitzchak 77; Piskeiy Teshuvos 135:16