In cases where one may respond in the middle of Birkhot Keri’at Shema, she may only respond while reciting the main part of it, from the beginning until just before the conclusion. However, once one says “Barukh Atta Hashem” at the conclusion, she may not interrupt at all, for such an interruption truncates the berakha (BHL 66:3).
Similarly, when reciting the verses “Shema Yisrael…” and “Barukh Shem kevod…,” in which one accepts the yoke of heaven, one may not interrupt for anything, for they have the same status as the Amida, in which we do not interrupt at all (SA 66:1).
In any case of uncertainty in the middle of Birkhot Keri’at Shema or Pesukei De-zimra, it is best not to respond, for according to many poskim, even if it is permissible to respond, there is no obligation to do so (Peninei Halakha: Prayer, ch. 16 n. 4).
In the middle of the Amida it is forbidden to respond to any davar she-bikdusha, including Kaddish and Kedusha. However, one may remain silent and be attentive to the ĥazan’s Kaddish and Kedusha, for listening with kavana is considered like actually responding. However if interrupting the Amida to listen to ĥazan disturbs her kavana, it is better that she continue her silent Amida (Peninei Halakha: Prayer 17:15).
On weekdays, one must not interrupt between Ga’al Yisrael and the Amida for any davar she-bikdusha, for adjoining redemption to prayer helps save people from distress. However, on Shabbat, which is not considered a day of distress, there is less of a necessity to adjoin redemption to prayer, and according to most poskim one may interrupt to respond to devarim she-bikdusha. On festivals, which are days of judgment (on Sukkot, we are judged regarding water, on Pesaĥ regarding the harvest, and on Shavuot regarding tree fruits – see RH 16a), one may not interrupt between redemption and prayer (SA 66:9; Rema 111:1; Peninei Halakha: Prayer, ch. 16 n. 7).