Covering the head with the Tallis Gadol during Davening:
The letter of the law: It is disputed whether one must also cover his head and perform the Yishmaeili wrap with the Tallis, in addition to covering the body. Some Poskim rule that the Tallis must be large enough for one to perform the Yishmaeli wrap, for it to be obligated in Tzitzis. According to this opinion one must wear his Tallis in a Yishmaeli wrap for it to be considered that he is fulfilling the Mitzvah. However, according to those opinions who disregard this size requirement for the Tallis, there is no need to wear it in a Yishmaeli wrap, and rather one is to simply cover his head with the Tallis at the time of the blessing. Practically, we rule like the latter opinion [and hence one is not obligated to wrap himself with the Tallis in a Yishmaeli wrap even during the blessing, and is not even required to cover his head at all with the Tallis, with exception to the time of the blessing. Nevertheless, see end of this Halacha that the scrupulous are careful to cover their head with the Tallis throughout Davening. If one does not cover his head with the Tallis even at the time of the blessing it is possibly a blessing in vain.]
The custom: It is the custom of those particular in Mitzvos, and of all the Chassidim, to cover their head with the Tallis Gadol throughout the entire period of time that they are wearing it, in order so their head is not uncovered for even one moment. Doing so humbles ones heart and leads to fear of heaven. One who removes his Tallis from his head is like one who passes over the chance to perform a Mitzvah. One is not to uncover his head from the Tallis even if he is very hot. The Tallis is to remain on one’s head from the beginning of Davening until the end. Seemingly, this applies likewise during Kerias Hatorah. Nonetheless, the Rebbe Rashab was not accustomed to cover his head during the Keriah.
 Admur 8:5-6; The idea of a Yishmaeli wrap is first mentioned in Moed Katan 24a regarding a mourner. It is disputed as to whether this concept is relevant also to the wearing of a Tallis.
 Opinion in Admur 8:5; Geonim [brought in Baal Haittur Tzitzis 2:3 and Tur 8 and Beis Yosef]; Ritva brought in Nimukeiy Yosef Tzitzis; Rabbeinu Sadya Gaon brought in Kaf Hachaim 8:7; Tosafus Erechin 2b; Ridbaz 1343; Makor Chaim 8:4; See Shoel Umeishiv Gimel 3:128; Maharsham 4:5
 This means that one is to cover his head and face with the Tallis until below the mouth, by the cheek bones. [Admur ibid]
 Admur 8:5
The reason: As the Sages established the wording of the blessing made over the Tallis “to wrap oneself with Tzitzis,” hence implying that the Mitzvah is specifically to wrap the Tallis. Now, since any wrap which is not the Yishmaeli wrap is not termed as wrapping but rather as wearing [see Moed Katan 24a], therefore one must wear the Tallis like a Yishmaeli. According to this opinion, the Tallis Katan of today is exempt from Tzitzis, being that the command only applies to clothing that is large enough to be wrapped like a Yishmaeli. [Admur ibid]
 Admur 8:5
 Opinion in Admur 8:6; Michaber 8:2-3; Tur 8 in name of Ba’ll Ittur Tzitzis 2:3, Nimukeiy Yosef ibid; Terumos Hadeshen 45; Mahark; Iggur; Mahariy
 Admur 8:6; Michaber 8:2
The reason why according to this opinion the blessing is Lehisatef Betzitzis: The reason the Sages instituted to recite the wording of “Lehisatef Betzitzis” is because it was the custom in the times of the Sages, which established this blessing, to wrap their heads in the Tallis. [Furthermore] even in their times they did not wrap their heads in the Tallis in a Yishmaeli wrap, but rather [they covered their heads with the Tallis] as is commonly done by people that wrap themselves in their clothing and go about their work. At times they cover their heads and at times their heads are uncovered. Therefore, we also, although we recite the wording of “Lehisatef Betzitzis”, nevertheless we do not have to wrap ourselves more [than the original Sages]. [Admur ibid]
 So is implied from Admur ibid that the head must be covered according to all [at least during the blessing] and the dispute is only regarding whether it must be covered in a Yishmaeli wrap and so proves Radbaz 1:143 that the head must be covered from the above wording of Admur which is based on the Tur and also from the fact the Nussach of the blessing is Lihisatef Betzitzis. See also Matzos Shmurim p. 23b “The main purpose of the Tallis Gadol is to cover the head. Unlike those few Shotim who only garb their body in the Tallis Gadol and not their head, and it is a great mistake in their hands, and they are saying a blessing in vain, as how can they say the blessing of Lihisateif, if they are not garbing their head”; However Tzaruch Iyun from Chayeh Adam 12:4 that one is Yotzei Bedieved even if he said Lihisatef on a Tallis Katan, and that he may do so even Lechatchila, even if he does not do Atifas Yishmaeilim. The Shaareiy Teshuvah 8:3 writes “If one does not cover the head when wearing the Tallis by the blessing, he has not fulfilled the blessing.” However seemingly he is referring to the case of the Maasas Binyamin, in which only the shoulders are covered and not the body.
 See Matzos Shmurim p. 23b “The main purpose of the Tallis Gadol is to cover the head. Unlike those few Shotim who only garb their body in the Tallis Gadol and not their head, and it is a great mistake in their hands, and they are saying a blessing in vain, as how can they say the blessing of Lihisateif, if they are not garbing their head”
 Toras Menachem 18:106
 Bach 8; Taz 25:2; Olas Tamid 8:3; Matzos Shmurim p. 23b “The main purpose of the Tallis Gadol is to cover the head. Unlike those the few Shotim which only garb their body in the Tallis Gadol and not their head, and it is a great mistake in their hands, and they are saying a blessing in vain, as how can they say the blessing of Lihisateif, if they are not garbing their head”; Radbaz 1:343; Shaareiy Teshuvah 8:3; M”B 8:4; Ketzos Hashulchan 7:4; Toras Menachem 18:106 [brought in Shulchan Menachem 11:36]; See Shaareiy Teshuvah 8:3 and Kaf Hachaim 8:9 for different customs in this regard
 Bach ibid
 Taz ibid
 Magen Gibborim 91:3 in name of Meiri; Chavos Yair 53:1
 Elya Raba 8:4; Poskim in Kaf Hachaim 8:10; Ketzos Hashulchan ibid
 See Otzer Minhagei Chabad Tishrei 211; Reshimos Devarim 2:102