Talking during Kerias Hatorah:
Once the reader has begun to read the Torah it is forbidden for the congregants to speak. [Furthermore, some Poskim rule that even prior to the start of the reading, once the Sefer Torah is opened, it is forbidden to speak.]
Between Aliyos: It is forbidden to speak even between the Aliyos, [even when the Mi Shebeirah is recited, and hence from the commencing of the reading until the conclusion of the final reading, speech is prohibited]. This applies even to words of Torah. It is however permitted for one to be lenient to learn Torah quietly to himself in between the Aliyos. However, once the blessings are recited he must be quiet and listen.
Shnayim Mikra Echad Targum: There are those which permit to read Shnayim Mikra Echad Targum [to themselves] during the reading of the Torah on Shabbos. [Others however forbid doing so. Practically one is not to do so, as it is proper to listen to the words being read by the Baal Koreh. One may however read along with the Baal Koreh, and doing so is praiseworthy. It is likewise allowed to read Shnayim Mikra between the Aliyos.]
Halachic rulings: It is forbidden for a Rav to give Halachic ruling to an asker during the reading of the Torah, although he may do so between the Aliyos. If however the matter involves stopping a person from currently doing a sin then it is allowed for him to answer even in middle of the reading. Nevertheless one is to first try to stop the person through a hint, and only if he is unable to do so should he actually speak during the reading.
Once the reader has begun to read the Torah it is forbidden for the congregants to speak at all, even words of Torah, until the conclusion of the final reading. Some Poskim rule that even prior to the start of the reading, once the Sefer Torah is opened, it is forbidden to speak. It is forbidden to speak even between the Aliyos, and even when the Mi Shebeirah is recited. It is however permitted for one to be lenient to learn Torah quietly to himself between the Aliyos. However once the blessings are recited he must be quiet and listen.
May one speak during Kerias Hatorah if he already heard the reading in a different Minyan, or plans to hear it later on?
It is forbidden to speak to others during the reading even if one already heard Kerias Hatorah with a Minyan, being that this will disturb others. Furthermore, some Poskim rule one may not even learn Torah quietly to himself during the reading and is thus required to listen to the reading a second time. Practically however, if there are ten people other than him listening to the reading then he may learn Torah quietly to himself during the reading. He should also make it apparent that he has already heard the Torah reading or plans to do so in a different Minyan.
May a Rav give a Drasha between Aliyos?
A Rav may give a Drasha which involves the Mitzvah of Tzedaka in order to motivate the congregants to donate money to the Shul upon them receiving their Aliyah.
The severity of the sin of speaking during Kerias Hatorah:
Speaking during Kerias Hatorah is a very severe sin. It causes one’s prayer to be an abomination and not be acceSee Piskeiy Teshuvosed by Hashem. It belittles the Torah and Hashem, and one’s punishment will be sure to come. It banishes the Shechina from the Shul, and causes death and poverty amongst the Jewish people. On the other hand one who respects the Torah and its reading causes that the Torah arouses Divine mercy upon him and his family in both spiritual and material matters.
Free Translation of the words of the Rebbe Rayatz on the severity of speaking during the Torah reading:
It is thus incumbent upon the reader of the Torah to be well versed in all the laws of Kerias Hatorah, as this matter touches one’s very soul. On this the verse states that life and death is in the hands of the tongue. Just as the reward is very great for one who reads the Torah properly, according to law, so too is the great and immense retribution against one who belittles the reading of the Torah properly and does not place vast effort to know all the tunes of the reading. One who does not do so is Heaven forbid considered like one who causes the masses, which are the listeners of his incorrect reading, to sin. On this the verse states that life and death is in the hands of the tongue. Now, this likewise applies to those that listen to the reading of the Torah, that they need to listen to the reading from a Sefer that is in their hands, and they need to hear each and every word. It is known the great and immense consequences in this world and the next to those who are not careful in this. It is explained in Sefarim that listening to the Torah reading properly affects the blessings one receives in Banaiy/children; Chayaiy/Health; and Mezoni/Parnasa. One who demeans the listening of the Torah is a brazen person which expels the king from his own palace. One who speaks to a friend is causing the masses to sin and increases Heaven forbid and Heaven forefend, death and poverty amongst the Jewish people.
 Michaber 146:2; Sotah 39a; Zohar Vayakhel p. 206
 This prohibition applies according to all opinions regarding mundane words, as it is only regarding words of Torah in which there is a dispute.
 M”A 146:3 based on Gemara ibid; Gr”a; Soles Belula 146:3; M”B 146:4
Other opinions: Some Poskim rule the prohibition of speech only begins from the time that the reading commences. [Michaber ibid as explained in Beis Yosef; Rashi on Gemara ibid; Elya Raba 146:3; Mateh Yehuda146:3; Derech Hachaim 3; Shaareiy Efraim 4:11; Kaf Hachaim 146:8]
 1st opinion of Michaber ibid and his final ruling; Peri Chadash; Shelah 77, brought in M”A 146:5; Gr”a in Maaseh Rav; Aruch Hashulchan 146:6; M”B 146:15; Achronim as brought in Kaf Hachaim 146:13; Rebbe Rashab in Modaah Raba [printed in Siddur Im Dach p. 644]
Background and other opinions in Michaber: The Michaber records five opinions regarding learning Torah during the reading. 1) It is forbidden to do so in any circumstance; 2) Some opinions [Rashi] permit one to learn quietly. 3) Some opinions [Bahag] rule that if there are ten other people listening to the reading, it is permitted for one to speak [words of Torah-Rama]. 4) Some opinions [Rif] rule if one’s occupation is Torah learning he may learn Torah. 5) Some opinions [Talmidei Rabbeinu Yonah] rule that it is permitted for one to learn Torah during the reading if prior to the opening of the Torah he turned his face away from the Torah and made himself appear that he does not desire to hear the reading but rather to learn, and he began to learn. In the Beis Yosef 146 he concludes that it is valid to rely on all of the above Sages. However the Michaber ibid concludes “The proper ruling to follow is that by all the Parshiyos it is befitting for a meticulous Jew to pay attention and listen to the reading.” The Rebbe Rashab in Modaah Raba [printed in Siddur Im Dach p. 644] explains that based on the Kelalei Haposkim it is evident that the Michaber rules like the first opinion. So is also the ruling of all the Achronim to be mentioned below that one may only be lenient to learn quietly between the Aliyos. [Kaf Hachaim 146:13] The Shelah ibid concludes that the Torah Scholars that learn Torah during the reading indirectly cause others to speak during the reading and will be punished for doing so.
Parshas Zachar and Parah: According to all opinions the reading of Zachar and Parah must be listened and heard by the congregants [even by one who desires to learn Torah based on one of the above allowances], as the reading of these Parshiyos with a Minyan are Biblical. [Michaber ibid]
 Olas Tamid 146:3; Beis Yosef in name of Rashba; Kaf Hachaim 146:12
 Michaber ibid
Other opinions: Some Poskim rule it is permitted to speak even mundane words between the Aliyos. [Peri Chadash 146:2; Bach as brought in Beir Heiytiv 146:3; P”M 146 A”A 7]
 Mareh Yichezkal 26; Kaf Hachaim 146:15
A long Mi Shebeirach: In today’s times that the Mi Shebeirach can take quite some time, some justify those that are lenient to speak necessary words during this time, even if they are of mundane content. This however only applies to a short interjection that will not turn into a long conversation that will interfere with the reading. [See other opinions in previous footnote; Aruch Hashulchan 146:3; Shulchan Hatahor 146:1; Piskeiy Teshuvos 146:3] The Kaf Hachaim 146:10 completely negates their opinion.
 Beis Yosef 146
 The reason: As we suspect the person will continue his conversation even after the reading resumes. [Beis Yosef; M”B 146:6]
 Drashos Maharil; Kneses Hagedola 146:1
Other opinions: Some Poskim rule it is permitted to speak words of Torah between the Aliyos, and that so is the custom. The reason for this is because the entire reason for the prohibition during the reading is in order not to disturb others, and hence in-between the reading there is nothing to suspect for. [Bach 146, brought in M”A146:3; M”B 146:6; Peri Chadash 146:2] According to this opinion it is permitted for one to learn even aloud. [Kaf Hachaim 146:10]
 Seder Hayom; Elya Raba 146:4; M”B 146:6; Chesed Lealafim 146:13; Kaf Hachaim 146:10 and 13
Other opinions: From the Maharil ibid it is implied that he forbids learning even quietly to oneself.
 Elya Raba ibid
 Admur 285:8
 Michaber 146:2 as rules Murdechaiy; Hagahos Ashriy; Reb Yehuda Hachasid; Terumas Hadeshen.
The Elya Raba rules that not only is this allowed but it is a mitzvah Min Hamuvchar. However the Mamar Murdechaiy argues on the ability to call this leniency a Mitzvah Min Hamuvchar, See Biur Halacha 285 “Yachol”.
 So as not to disturb the listeners. [Peri Megadim, brought in M”B 146:11]
 It is permitted to read even a different section in that Parsha than the section which the Baal Korah is reading. The reason for this allowance is because at the end of the day the reader is involved within the same topic as is the Baal Korah. [Peri Megadim, brought in M”B 146:11] This allowance applies even if he is part of the 10 listeners. [Magen Avraham 146:5 in name of Terumas Hadeshen]
 Peri Chadash; Magen Avraham [146:5] in name of Shalah is stringent in this. [M”B 146:15]
 Final ruling of Michaber 146:2 as explained in M”B 14 to be referring also to Shnayim Mikra; M”B 285:14
 Mateh Moshe; Magen Avraham 146:5; M”B 146:15
 Poskim ibid; M”B 146:15; 185:14
 M”A 146:4 in name of Rif; M”B 146:5
The reason: As one can delay the ruling until after the reading. [P”M 146 A”A 4]
Other opinions: Some Poskim rule it is permitted to temporarily recite a Halacha or give a Halachic ruling during the reading. [Darkei Moshe 146:1]
 Elya Raba 146:4; Derech Hachaim 3; Shaareiy Efraim 4:11; M”B 146:6; Kaf Hachaim 146:9
 P”M 146 A”A 4; Levushei Serud ibid; Derech Hachaim ibid; Shaareiy Efarim ibid; M”B 146:5; Kaf Hachaim 146:9 and 11
 Shaareiy Efarim ibid; M”B 146:5;
 M”B 146:7 in name of P”M 146 and Gr”a
 Piskeiy Teshuvos 146:4 based on the lenient opinions in Michaber ibid
 Kaf Hachaim 146:11
 Biur Halacha 146:2 “Vehanachon”
 Shelah Hakadosh p. 132
 Rebbe Rayatz in translated Mamar brought next
 Rebbe Rashab in Modaah Raba [printed in Siddur Im Dach p. 644]
 Sefer Hamamarim 1937 p. 263