Writing, text messaging, Whatsapping, during Davening:\
It is forbidden to talk during Davening, once one has begun Baruch Sheamar, until after Shemoneh Esrei. The question is asked regarding the status of writing, and if it is likewise forbidden to write, or send text messages, during Davening, just as it is forbidden to speak, or if writing is of lesser level, and hence permitted to be done.
During Shema: It is forbidden to make an interval during Kerias Shema even if he will not be saying any words, unless it is for the sake of a slight Mitzvah in which case if he is past the first paragraph of Shema [i.e. Vehayah] he may make a non-verbal interval. [Accordingly, it is forbidden to stop during the reading of Shema for the sake of writing, or sending text messages through SMS or Whatsapp, unless doing so contains a slight Mitzvah and he is not within the first paragraph.]
Past Baruch Sheamar-During other areas of Davening: Initially, one may not make an interval during any part of Davening [past Baruch Sheamar], even if he will not be saying any words. Accordingly, one is not to stop in middle of Davening for the sake of writing [or sending text messages through SMS or Whatsapp]. However, in a time of real need, one may write during Davening, past Baruch Sheamar [so long as he is not in the midst of the first paragraph of Shema, or in Shemoneh Esrei, or between Gaol Yisrael and Shemoneh Esrei].
Initially, one is not to write or send text messages during Davening unless it is a time of real need, and he is not within the first paragraph of Shema, Shemoneh Esrei, or between Gaol Yisrael and Shemoneh Esrei.
 Admur 51:4 and 53:3; Rama 51:4; Levush 51:5
 Admur 63:7; Michaber 63:6; Yuma 19b
 See Salmas Chaim 49; Yagel Yaakov 10; Betzel Hachochma 4:88; Beir Moshe 2:7 [there he permits writing with exception to 1st paragraph of Shema]; Yabia Omer 9:10; Teshuvos Vehanhagos 2:40; Shevet Hakehasi 1:77; Piskeiy Teshuvos 51:8; 66:1
 Beis Oved 51:3; Makor Chaim 51; Kaf Hachaim 51:17; See Admur 63:7
 The reason: As although writing is not like talking regarding its quality of interval [See Admur 47:3 regarding Birchas Hatorah], and thus does not receive the same level of severity, nevertheless, initially, one is not to make any interval during Davening, even if it does not involve speech, just as is the law regarding Shema. [Beis Oved 51:3; Makor Chaim 51; Kaf Hachaim 51:17; See Admur 63:7]
 The reason: As the main prohibition of Hefsek is specifically regarding speech. [See Admur 51:4] And thus we rule that one may stop to make non-speech intervals even during Kerias Shema, after the first Parsha, if it is for the sake of a Mitzvah [Admur 63:7] even though one may never make an interval for speech even if it is for the sake of a Mitzvah, even in Pesukei Dezimra. [Admur 51:4] Certainly, then this applies during Pesukei Dezimra. [Beis Oveid ibid] Likewise, this allowance also applies in a time of need. [Poskim ibid]
 Admur 63:7; Vetzaruch Iyun if the Heter of a need applies to the 2nd paragraph of Shema or only if it contains a slight Mitzvah, as rules Admur there.
 See Admur 96-97; 104
 Admur 111:1