Is one obligated to wear Tefillin when saying Shema before Davening in order to fulfill the obligation of Shema?
If one is reciting Shema prior to sunrise, prior to Davening, he may read Shema even if he is not yet wearing Tefillin. If, however, one is reciting Shema after sunrise, he is not to say it until he puts on Tefillin. [Nevertheless, the custom amongst most Chassidim is not to wear Tefillin when saying Shema prior to Davening, even after sunrise. However, some Chassidim are accustomed to wear Tefillin upon reciting Shema prior to Davening, and so was the directive of the Rebbe Rashab and Rebbe Rayatz. This is not the widespread Chabad custom.]
Is one to wear Tefillin when reciting Shema as part of Karbanos?
If one is not fulfilling his obligation of Shema with this recital, then even according to the stringent opinion brought above, he is not required to wear the Tefillin while reciting it. If, however, one is planning to fulfill his obligation with this reading then this enters into the same discussion as above.
According to the stringent opinion brought above, may one say the first verse of Shema for the sake of fulfilling one’s obligation without wearing Tefillin?
Even according to the stringent opinion brought above, one may recite the first verse of Shema without Tefillin.
Is one required to wear Tefillin when reading Shema after Davening, such as by Shnayim Mikra and the like?
No. The above obligation only applies when one is reciting Shema for the purpose of fulfilling his obligation. If, however, he is simply reciting it to read from the Torah, there is no obligation to wear Tefillin. However, some were stringent even in such a case.
 Admur 58:4 “One is to read at least the first Parsha before sunrise even if he did not yet wear Tallis and Tefillin” 58:5 “However if one is reading it after sunrise…”; Based on Levush 58:2
The reason: As it is a Mitzvah to read Shema in its proper time before sunrise, and is hence similar to the ruling in 66:11 that one may say Shema without Tefillin if he does not have Tefillin and is worried that the time will pass. Vetzaruch Iyun if one must wear Tefillin if he has much time until sunrise and is able to do so, as in 66:11 Admur forbids reading the Shema without Tefillin unless one suspects the time will pass. Thus, perhaps this entire law of Admur refers to one who does not have time or ability or desire to wear them before sunrise, although ideally, he should do so. Vetzaruch Iyun!
Other opinions: Some Poskim rule one is not to read Shema prior to sunrise without Tefillin. He is rather to read only the first verse and Baruch Sheim. [Kaf Hachaim 58:8]
 Admur 66:11; Siddur Admur [Letter 22]; M”A 66:12; Degul Merivava and Rav Akiva Eiger, brought in M”B 46:33; Kaf Hachaim 25:27
The reason and explanation: Admur in the Siddur and 66:11, based on M”A ibid, rules that it is better to Daven in private with Tefillin than to Daven with a Minyan but without Tefillin due to Eidus Sheker. Likewise, he implies that one is not to say Shema without Tefillin unless the time of Shema is passing. From here we learn that saying Shema without Tefillin is Eidus Sheker even if he plans to wear Tefillin later on and say Shema again while wearing them. So is also proven from Torah Or Vayakhel in that one cannot draw down the Penimi without first having worn Tefillin and drawing down the Makif. Now, Admur 58:4-5 makes it evident that this refers only when reading Shema after sunrise as in 58:4 he permits reading Shema before sunrise without Tefillin while in 58:5 he writes that if it is after sunrise one is to read Shema as soon as possible with Tallis and Tefillin. Vetzaruch Iyun as to the difference between before and after sunrise, that before sunrise it may be said without Tefillin and after sunrise it may not! Perhaps then one must say this entire law of Admur refers to one who does not have time or ability or desire to wear them before sunrise, although ideally, he should do so. Vetzaruch Iyun!
 Chozeh Melublin [brought in all the following Sefarim]; Beis Yitzchak 17; Os Chaim Veshalom 25:6; Rebbe in Toras Menachem 28th Sivan 1952, vol. 6 p. 5, printed in Shulchan Menachem 1:125-130; See Rameh in Alfasi Zuta Brachos ibid; Miasef Lechol Hamachanos 25:31; Ashel Avraham Butchach 25 that a proof can be brought from Tishe Beav; Minchas Yitzchak 2:108; Yabia Omer 1:4 in name of many Poskim; Piskeiy Teshuvos 25:8
The reason: As it is only considered false testimony to say the morning Shema without Tefillin if one does not plan to wear Tefillin at all that day, and hence plans to nullify the Mitzvah that he read in Shema. If, however, one plans to wear Tefillin later on, then it is not considered false testimony at all. [Rebbe in Toras Menachem 28th Sivan 1952] A proof for this can be brought from the fact that the Gemara [Brachos 14b] compares saying Shema without Tefillin to bringing a Karban without Nesachim, now just as one can bring the Nesachim after the Karban, so too he can wear Tefillin after Shema. [Chozeh Melublin brought in Sefarim ibid] Furthermore, one is to specifically say Shema before wearing the Tefillin as the Tefillin are higher than the saying of Shema and one is hence to follow the order of Maalin Bakodesh to fist say Shema and then wear Tefillin. [Os Chaim Veshalom ibid; Rebbe ibid]
 Os Chaim Veshalom ibid that so is the custom of some and that doing so is a Hiddur Miztvah
 Directive of Rebbe Rashab in Kuntrus Eitz Chaim 25 “After wearing Tefillin and Kerias Shema and after drinking tea they are to learn for two consecutive hours”; Igros Kodesh of Rebbe Rayatz letter 3302 “Certainly they are careful to say Kerias Shema Ketana with Tefillin”; Sichas Shelach 1952 “The Rebbe Rayatz told me that his father the Rebbe Rashab would read Shema in the morning with Tefillin
 Degul Merivava and Rav Akiva Eiger, brought in M”B 46:33; Binyan Olam 7; Kaf Hachaim 25:27
 As Admur 25:1 rules that the false testimony is due to the verse of Ukeshartam, and hence if one is not reading it there is no false testimony; Kaf Hachaim 25:27 according to Tosafus and Ran
Other opinions: Some Poskim rule that even the first verse of Shema is not to be said without Tefillin, if one intends to fulfill his obligation. [Kaf Hachaim 25:27 based on Rashi and Maadnei Yom Tov]
 Degul Merivava and Rav Akiva Eiger, brought in M”B 46:33; Binyan Olam 7; Kaf Hachaim 25:27; Os Chaim Veshalom 25:6; Rebbe in Toras Menachem 28th Sivan 1952; So is also proven from Admur 34:5 and Siddur Admur that allows saying Shema while wearing Tefillin of Rabbeinu Tam and considers it a Hiddur.
 Minhag Hageonim to wear Tefillin during Shema of Maariv, brought in Hagahos Maimanis on Rambam Tefillin 4 in name of Baal Haittur, brought in Beis Yosef 25; Custom of Chasam Sofer to not way Shema while wearing Rabbeinu Tam Tefillin, recorded in Likkutei Chaver Ben Chaim, brought in Os Chaim Veshalom ibid; Minhagei Chasam Sofer 1:22 that he would not say Shnayim Mikra of Shema without Tefillin.
The reason: As the Biblical Mitzvah of wearing Tefillin applies throughout the entire day and hence whenever one reads Shema without Tefillin he is testifying falsely. [Os Chaim Veshalom ibid; Rebbe ibid]