Talking and learning Torah during Kedusha:
It is forbidden to speak in middle of Kedusha. Even if there is a Minyan present aside for him, nevertheless it is forbidden. It is even forbidden to learn Torah during Kedusha [even in one’s thought].
Where in Kedusha is it forbidden to speak/learn: It is permitted [to speak and learn Torah] while the Chazan is singing a Niggun, although not during the time that he is saying the words of Kedusha. [The words of Kedusha in which it is forbidden to speak or learn include the sentence of Nakdishach, Kadosh, Baruch and Yimloch] however the dialect that is added on Shabbos [and Yom Tov] is not considered part of Kedusha [and hence there is no prohibition to speak or learn while it is recited and certainly one may think words of Torah at this time]. Nevertheless, it is forbidden to speak between Kadosh and Baruch [even during the additional dialect added on Shabbos, and even if the Chazan is singing]. Furthermore, it is good not to speak at all [even of Torah] throughout the entire Kedusha until after the Amen of Hakel Hakadosh. [This applies even if one alreay Davened and is answering Kedusha a second time.]
May one even verbalize words of Torah while the Chazan is singing, or by the added Nusach of Shabbo/Yom Tov?
Is it proper to learn words of Torah in one’s mind while the Chazan is singing etc?
May one who is in middle of Davening continue to Daven during the singing and added dialect of Kedusha?
 Admur 125/2; M”A 125/1; M”B 56/1; 125/1; Ketzos Hashulchan 22/8
 Admur 56/7 and 125/2; Rama 125/1; Mahariy Abuhav; Shivlei Haleket 8 in name of Miseches Derech Eretz Zuta
The severity: Anyone who speak during Kedusha on him the verse [Yeshaya 43/22] states “And not to me did you call Yaakov..”, as explained in chapter 56/7. [Admur ibid] This verse emphasizes that Beni Yisrael are not calling to Hashem in prayer but rather to the foreign G-ds, and hence one who speaks during Kedusha is comparable to not only one who does noyt pray, but on the contrary, to one who is praying to a foreign G-d. [See Rashi and Radak on verse ibid] One time Eliyahu Zal was found [by Rav Aacha] and with him were 4000 camels carrying a load. He was asked “What are these camels carrying?” and he replied that they are carrying wrath and anger. They continued to ask “Why and for what purpose?” and he told them that this is to take avengence with wrath and anger against those who speak between Kaddish and Barchu, Kedusha and Kedusha, Kadosh and Baruch, between a Bracha and a Bracha, between a chapter and a chapter, and between Amen Yihei Shmei Raba and Yisbarech.” [Admur 56/7; Manhig Tefila 4 in name of Midrash; Shivalei Haleket 15; M”B 56/1]
 Admur 125/2; M”A 125/1; Hagahos Yeish Nochlin [Yeish Nochlin is of the father of Shelah, and the Hagahos is of his son Yaakov, the brother of the Shelah]
 M”B 125/1
The reason: As one must listen to the words being said by the Chazan. [M”B ibid]
 See Admur 125/1; M”A 125/1; M”B 125/1
 So is implied from Admur ibid that even speaking is permitted [after Baruch, during the Niggun or added Nussach], and certainly verbalizing words of Torah, and on this is the novelty of the Maharil [brought next] that it is best not to speak at all, even during this time. However from M”B ibid it is implied that speaking is forbidden by all parts, and only thinking words of Torah is permitted. See Piskeiy Teshuvos 125/3 footnote 20 that although so is implied from Admur and others, it is implied from the source of M”A ibid in Yesih Nochlin that speaking is forbidden, and so explicitly rules the Makor Chaim 124/4 that it is forbidden to speak at all, even of a Mitzvah until after Amen of Hakeil Hakadosh. Afterwords I saw that so is explicitly written in Yeish Nochlin and the Hagahos that only learning in one’s thought is permitted and not to verbalize. However from Adur it is clearly implied that even verbalizing is permitted as otherwise there is no novelty in his continued statements of not speaking between Kadosh and Baruch etc. Vetzaruch Iyun!
 M”B ibid that one is not required to listen to its recital.
 Admur ibid; M”A ibid; M”B ibid;
 Admur 56/7 and 125/2; Manhig Tefila 4 in name of Midrash
 Implication of Admur ibid; M”B ibid; Makor Chaim ibid; Piskeiy Teshuvos 125/3 footnote 20
 Admur 125/2; Maharil, brought in Darkei Moshe 125/2; Elya Raba 125/5; Kaf Hachaim 125/16
 See Kaf Hachaim ibid
 See footnote in the Halacha above that from Admur ibid it is implied that it is allowed from the letter of the law, although it is proper not to do so. However other Poskim rule that it is forbidden to do so.
 Yeish Nochlin ibid
 See Piskeiy Teshuvos 67 footnote 16 and 125 footnote 19 in name of Chassidishe Sefarim that doing so “transgresses” Lo Samod Al Dam Reiacha, and Hakeim Takim Imo.
 Implication of Admur ibid; Piskeiy Teshuvos 125/3 based on makor Chaim, unlike Rav SZ”A in Halichos Shlomo 8/38 that says one may continue Davening