1. If one will only receive Tefillin after Zeman Shema/Tefila, when is he to say Shema or Daven?[1]

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.[2]

[1] 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]

[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]