If one will only receive Tefillin after the Minyan, when is he to Daven:
If one does not have Tefillin and the congregation has begun to Daven, it is better for him to delay his Davening until after the Minyan concludes and then borrow Tefillin from one of the Daveners than for him to Daven with the congregation without Tefillin. If however the time of Shema or Davening will pass by the time he receives the Tefillin, then he is to recite Shema/Daven without Tefillin, as stated in next Halacha.
It is better to Daven in private with Tefillin than to Daven with the congregation without Tefillin. If however the time of Shema or Tefila will pass, then he is to say Shema and Daven without Tefillin.
If one has Rabbeinu Tam Tefillin but not Rashi, is it better to Daven in private with Rashi than to Daven with the Minyan wearing Rabbeinu Tam?
Some Poskim rule that in such a case it is better to Daven with the Minyan while wearing Tefillin of Rabbeinu Tam.
If one does not have Tefillin and he is part of the six Daveners for the Minyan, is it better that he Daven without Tefillin in order so the Minyan can take place?
If one will only receive Tefillin after Zeman Shema/Tefila, when is he to say Shema or Daven?
If one does not have Tefillin and suspects that the time of Shema will pass by the time he receives the Tefillin, then he is to recite Shema without Tefillin. Likewise, if one does not have Tefillin and suspects that the time of Tefila will pass by the time he receives the Tefillin, then he is to Daven without Tefillin.
 66/11; Siddur Admur [letter 22 in Raskin]; M”A 66/12; M”B 66/40; Ketzos Hashulchan 8/3
Other Poskim: Some Poskim rule it is better to Daven with the congregation without Tefillin than to Daven with Tefillin in private. [Elya Raba 58/5; Maharsham 3/359; See Peri Chadash 496/25 and Chayeh Adam 110/4]
 The reason: As it is better that one read Shema and Daven with Tefillin, thus accepting upon himself the complete Yoke of Heaven, than to Daven with the Minyan without Tefillin and testify falsely about himself. [Admur ibid]
 Machazik Bracha 34/6 in name of Michtam Ledavid 4
 Piskeiy Teshuvos 25/9; See Admur in 90/17 that the Mitzvah of Davening with a Minyan which contains the greatest positive command of sanctifying Hashem’s name in public, pushes off even a negative command of not freeing a slave. [This is in contrast to other Poskim, such as Michaber Yoreh Deah 267/79 who do not view any special advantage in Davening with a Minyan regarding pushing off this negative command, and rather rule that all Rabbinical Mitzvos may push off this command of not freeing a slave.]
 Admur 66/11 and 80/3; Siddur Admur [letter 22 in Raskin]; M”A 66/12; Levush 58/2; M”B 25/14, 46/33, 66/40; Ketzos Hashulchan 8/3; See Mor Uketzia 25; Beir Moshe 5/5
Other Poskim: Some claim it is better to Daven with Tefillin after the Zeman than to Daven without Tefillin before the Zeman. Practically, they are incorrect. [Levush 58/2]
 The reason: As the prohibition of saying Shema and Davening without Tefillin is only Rabbinical, and is only initially forbidden if one has Tefillin available. However if one is unable to wear the Tefillin during the prayer, then certainly he cannot use this reason to nullify a Biblical command. [Levush ibid] As the Mitzvah of Tefillin and Shema are two separate Mitzvos that do not prevent each other from being fulfilled. Furthermore, there is even no prohibition of Eidus Sheker involved in such a case, as explained the Levush ibid. [M”B 46/33]