Hefsek-Making an interval to answer Amen and the like:
Complete Hallel: When the complete Hallel is recited, the laws of making a Hefsek [speech interval] during Hallel has the same laws as a Hefsek during the reading of the morning Shema. This applies for both the laws of Hefsek within individual paragraphs and between paragraphs.
Half Hallel: When the half Hallel is recited, such as on Rosh Chodesh and Chol Hamoed Pesach, then it has the same laws of interval of between paragraphs. [Some learn this to mean that it has the same status as between the paragraphs of Shema. Others learn this to mean that it has the same status as Pesukei Dezimra. Practically, one may stop to answer everything that one can answer during Shema, which includes: Amen Yihei Shimei Raba and Amen of Daamiran Bealma of Kaddish; Kadosh Kadosh, Baruch and Yimloch of Kedusha; Borchu; The three words of Modim Anachnu Lach; Amen for Birchas Hatorah, Hakeil Hakadosh and Shomeia Tefila. One may make an interval even in the midst of a verse, although in the event that one did so he is to return to the beginning of that verse.]
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 Admur 488/3; Michaber/Rama 422/4
 Admur ibid; Rama ibid
The reason: As the recital of Hallel on these days is a Rabbinical obligation and hence receives a stricter status. [Admur ibid]
 Admur ibid; Peri Chadash 422; Kaf Hachaim 422/47
 Michaber 422/4 regarding Rosh Chodesh “One may ask Shalom even in the middle and for one who he must respect, and he may answer Shalom to any individual.”; Admur ibid that Chol Hamoed Pesach has the same status as Rosh Chodesh.
The reason: As on these days the recital of Hallel is only a Minhag and hence has a lesser stringency of Hefsek. [Admur ibid]
 Hefsek Betefilah 4/10 [p. 80] and p. 196; Dinei Uminhagei Rosh Chodesh Chabad 8/12 based on Admur 66/5 [and Chayeh Adam 20/4] that one may not make an interval of Amen between the paragraphs of Birchas Shema; Hiskashrus 441
 Nitei Gavriel Pesach 7/12 [p. 69]; Yabia Omer 2/32; The Peri Megadim 51 and glosses of Rav Akiva Eiger rule it is permitted to make an interval of Amen between the paragraphs of Birchas Shema. [See M”B 66/23]
 See Admur 66/4-5; Siddur Admur
 Admur 66/4; Kaf Hachaim 422/46
 Ketzos Hashulchan 18/2