Calling up relatives for Aliya’s:
From the letter of the law it is permitted to call two relatives to the Torah for an Aliyah one after the other. This applies whether they are brothers or father and son. However the custom is to avoid doing so due to Ayin Hara. If however one does not call the two relatives by name then it is allowed. [Practically, however, the custom is not to call up relatives one after the other even if they are not called to the Torah by names. This prohibition applies even if the relatives claim they are not particular about Ayin Hara. It is however permitted to call up relatives for Aliyos if there is a break of an Aliyah in between in which a relative was not called up.]
Shevi and Maftir: One is not to call two relatives for Shevi and Maftir. [This however only applies by Maftir of Shabbos, in which one reads both Aliyos from the same Sefer Torah and therefore the Ayin Hara applies. If however the Shevi and Maftir are read from two different Sifrei Torah, as occurs on Yom Tov and whenever there are two Torah’s taken out on Shabbos, then the Aliya’s may be given to two relatives, one for Shevi and the second for Maftir. However when three Sifrei Torah are removed, relatives may not be called up for Shishi and Shevi, being that Kaddish is not recited in-between. Likewise, when two Sifrei Torah are removed during the week, relatives may not be called up for Shelishi and Revi, being that Kaddish is not recited in-between. However, in a time of need one may be lenient. In such a case the relative who received the previous Aliyah is to descend from the Amud before the new Aliyah is begun.]
Relatives such as a father and son, or siblings, are not to be called for an Aliyah one after the other. If there was another Aliyah in between it is permitted to do so. When twop Sifrei Torah are removed, it is permitted to call them up for Shevi and Maftir.
What relatives are included in the above prohibition against giving an Aliyah one after the other?
Father son: The prohibition applies to a father and son [whether one calls up the son after the father or the father after the son].
Grandfather and Grandson: Some Poskim rule it is permitted to call up a grandfather and grandson, or vice versa, one after the other [if they do not have the same name]. Other Poskim rule it is forbidden to call up a grandfather and grandson from his son, or vice versa, one after the other. However a grandson from his daughter is permitted even according to this opinion. Practically, one is to be stringent in this matter unless the community custom is to be lenient. In a time of need one may be lenient. Likewise, Bedieved, if the grandson/grandfather was already called up, he is to take the Aliyah.
Father/son in-law: It is permitted to call a father and son in-law to the Torah one after the other.
What is one to do if he was accidently called to the Torah after an invalidating relative [father/brother]?
If he already went up to the Bima then he is to accept the Aliyah. It is proper in such a case for the relative who received the previous Aliyah to descend from the Bima right away and not wait until after the current Aliyah. If he did not yet go up to the Bima then he is not to go up and rather another person is to be called up in his stead.
If one called a person for an Aliyah and he was not in Shul, may the previous Aliyas son/relative be called for an Aliya?
If one called a person for an Aliyah and he was not in Shul, may his son/relative be called up in his place?
May a child who is under Bar Mitzvah receive the Aliyah of Maftir if his father/relative received Shevi?
On Simchas Torah may relatives be called up one after the other?
The custom is to be lenient in this matter.
May two relatives be called up for Hagba and Gelila?
Yes. However one is not to call them both up by name or give them both a Mi Shebeirach.
 141/6; Kol Bo 20; Mordechai
Other opinions: Some Poskim rule it is forbidden from the letter of the law to call two relatives one after the other, being that they are considered invalid witnesses. [Orchos Chaim, brought in Beis Yosef; Ateres Zekeinim 141/3; P”M 141 A”A 8] According to this opinion/reason, all relatives that are invalid to testify for each other are likewise not to be called to the Torah one after the other. [P”M ibid] Practically, we do not rule like this opinion. [Kaf Hachaim 141/25 based on Gr”a who proofs from the Gemara that even Pesulkei Eidus may receive Aliyos, and so is the final ruling of Michbaer ibid who rules the prohibition is only due to Maaras Ayin.]
 Michaber ibid;
 Rama ibid regarding Shevi and Maftir; Emunas Shmuel 47; Elya Raba 141/7; Chesed Lealafim 141/16; Poskim in Kaf Hachaim 141/26; M”B 141/21 [see there however that this only applies in communities that never call up by name, however to initially not call up by name just for this purpose is forbidden, as this itself serves as a recognition. However , see Shaareiy Efraim 1/32 who writes one may be lenient in a time of great need, brought in Shaar Hatziyon 141/22]
 Kisei Eliyahu 141; Poskim in Kaf Hachaim 141/32 and so concludes Kaf Hachaim that so is the custom even in those communities that do not call the Aliyos by name; Yechaveh Daas 3/50
The reason: As nevertheless the name is mentioned by the Mi Shebeirach. [Kisei Eliyahu ibid]
 Hagahos Beis Yosef; Elya Raba 141/8; Birkeiy Yosef 141/7; Yosef Ometz 16/4; M”B 141/19; Shaareiy Efraim 1/6; Derech Hachiam 14; Kitzur SHU”A 23/13; M”B 141/19; Poskim in Kaf Hachaim 141/29
Other opinions: Some Poskim rule it is permitted for relatives to forgive their particularness on this matter. [Noheig Katzon Yosef, brought in Kaf Hachaim ibid; Aruch Hashulchan 141/8] Practically, we do not rule like this opinion. [Kaf Hachaim ibid]
 Implication of Michaber and Rama ibid; Mateh Yehuda 141/7; Machazik Bracha 141/4; Kaf Hachaim 141/30
Other opinions: Some communities are accustomed not to call up relatives for Aliyos even if there is a break of an Aliyah in between. Brought in Mateh Yehuda ibid] Practically, this is not the widespread custom and so is the custom in Egypt, Eretz Yisrael, Turkey, and most of the world, although those that have a custom to be stringent even in such a case are to follow it. Kaf Hachaim ibid]
 Rama ibid; Maharil
Other opinions: Some Poskim rule that one may call two relatives for an Aliyah one after the other for Shevi and Maftir being that the Kaddish is considered an interval in between. [Maharikash, brought in Kneses Hagedola 1431/5 and Kaf Hachaim 141/33] Practically, we are stringent in this matter as rule majority of Poskim. [Kaf Hachaim ibid] However some Poskim rule one may be lenient like this opinion in a time of need. [Toras Chaim Sofer 141; Eretz Tzevi 1/39; Piskeiy Teshuvos 141/5]
 Kneses Hagedola 141/5; Beir Heiytiv 141/6; Olas Tamid 141/13; Elya Raba 141/7; Poskim in Kaf Hachaim 141/33
Other opinions: Some Poskim rule that even in such a case that two Sifrei Torah are taken out one is not to call two relatives for an Aliyah one after the other. [Mateh Yehuda 141/7, brought in Kaf Hachaim ibid] Practcially we are lenient in this matter as rule majority of Poskim. [Kaf Hachaim ibid]
 Shaareiy Efraim 1/32; Hisorerus Teshuvah 1/67; Piskeiy Teshuvos 141/5
 Poskim ibid
 Toras Chaim Sofer 141; Hisorerus Teshuvah 1/67
 Michaber ibid
 Michaber ibid
 Kneses Hagedola 141/7; Olas Tamid 141/13; Elya Raba 141/8; Poskim in Kaf Hachaim 141/26
 Peri Chadash, brought in P”M 141/8; Machazik Bracha 141/5 that some are accustomed like Peri Chadash
 Kaf Hachaim 141/27
 Kneses Hagedola 141/8, brought in P”M 141/8; Olas Tamid 141/13; Elya Raba 141/8; Mateh Yehuda 141/7; Poskim in Kaf Hachaim 141/27
 Kaf Hachaim ibid
 Kaf Hachaim ibid
The reason: As the majority of Poskim prohibit it as well as danger is to be Halachiclaly viewed even more strcit than an Issur. [Kaf Hachaim ibid]
 M”B 141/19
 Shaareiy Efraim 1/33
 Pesach Hadvir 147; Piskeiy Teshuvos 141/4
Other opinions: Some Poskim are stringent in this matter. [Sefer Hachaim [Falagi] 11] Practically, the custom is to be lenient. [Pesach Hadvir ibid; Piskeiy Teshuvos ibid footnote 24]
 Kneses Hagedola 141/4; Hagahos Beis Yosef; Elya Raba 141/8; Peri Chadash 141/6; Mateh Yehuda 141/7; Derech Hachiam 14; Kitzur SHU”A 23/13; Poskim in Kaf Hachaim 141/28
 Toras Chaim Sofer 141/4; Piskeiy Teshuvos 141/4
 Shaareiy Efraim 1/33; M”B 141/18
 Shvus Yaakov 3/10
 The reason: As since another person was called after the relative, it is enough of an interval to eliminate any Ayin Hara, even though the person did not actually take the Aliyah. [ibid]
 Yosef Ometz 16/4; Poskim in Kaf Hachaim 141/31
 Shevet Hakehasi 2/65
 Kneses Hagedola 141/6; Olas Tamid 141/13; Elya Raba 141/7; Derech Hachiam 14; M”B 141/20; Poskim in Kaf Hachaim 141/34
 Shaareiy Efraim 1/32; Piskeiy Teshuvos 141/4
 Shearim Hametzuyanim Behalacha 23/10 in name of Avnei Chefetz 16; Piskeiy Teshuvos 141/5