Reciting Hallel together with the Minyan:
It is a Mitzvah Min Hamuvchar to read Hallel together with the congregation immediately after [Shemoneh Esrei of] the Shacharis prayer.
Reading Hallel with the congregation prior to Shacharis? If one came to Shul after the congregation completed the Shacharis prayer [of Shemoneh Esrei] and has reached the saying of Hallel, and has not yet Davened Shacharis, then there is an opinion who says that if there is no worry that the time of Shema will pass, it is best for him to first recite Hallel with the congregation, and afterwards Daven Shacharis. This applies even on those days that one who Davens without a Minyan according to all opinions recites the complete Hallel with a blessing. [Nevertheless, the Arizal was not comfortable with such an arrangement of reciting Hallel out of its proper order, and hence according to the Arizal one is never to read Hallel prior to Davening. Practically, the widespread custom amongst Chabad Chassidim is not to recite Hallel before Davening, as explained in the summary below.]
If one is in the middle of Davening: If one is holding in middle of Davening, past Baruch Sheamar, at the time that the congregation begins to read Hallel, he is not to make an interval in order to read Hallel together with them. [However, this only applies] on those days [i.e. all of Sukkos and Chanukah; 2 days of Pesach] that even one who is Davening without a Minyan recites the complete Hallel with a blessing. [However on those days that the Hallel is recited without a blessing when one is praying without a Minyan [i.e. Rosh Chodesh and Chol Hamoed Pesach], then one is to stop and recite the Hallel together with the congregation. He is however not to recite a blessing prior to the Hallel and is rather to fulfill his obligation with the blessing recited by the Chazan. If one has already completed Pesukei Dezimra and has begun Birchas Kerias Shema, then he may no longer make an interval to recite Hallel with the congregation, even on days that one reads the incomplete Hallel.]
One is to be particular to read Hallel together with the congregation immediately after Shemoneh Esrei. If one is holding prior to Davening, some Poskim rule he is to stop and recite Hallel together with the congregation. This applies for Hallel of all days. If one is holding within Pesukei Dezimra, then some Poskim rule by half Hallel [of Rosh Chodesh and Chol Hamoed Pesach] he is to stop and recite Hallel together with the congregation. Nevertheless, the Arizal was not comfortable with such an arrangement of reciting Hallel out of its proper order, and hence according to the Arizal one is never to read Hallel prior to Davening.
The Chabad Custom:
The Rebbe stated that no clear directive has been given with regards to the Chabad custom in whether one should say Hallel with the congregation prior to his Davening, if the circumstance occurs. Nevertheless, it is known that the Chabad Rabbeim would be careful to always pray with the same pace as the Minyan on Yom Tov in order to say Hallel with the congregation. This is despite the Rabbeim’s usual practice of praying at greater length than the Minyan. [Practically, the widespread custom amongst Chabad Chassidim is not to recite it before Davening.]
Should one who usually Davens in great length without the congregation do so on days that Hallel is said?
The Rebbe Rashab would Daven Shacharis of Yom Tov on pace of congregation in order to say Hallel with the congregation after Shacharis, at its appropriate time. [Seemingly, this would apply likewise on Rosh Chodesh, Vetzaruch Iyun.]
 Admur 488:3
 Admur ibid; 649:21 in parentheses “And say with it Hallel with the congregation”; Rama 422:2 “A person would be careful to recite Hallel with the congregation in order so he recite the blessing together with the congregation”; M”A 422:6; Beis Yosef 422; Kol Bo 52; Leket Yosher regarding one who does not have a Lulav for Hallel but will have afterwards, that he should still say Hallel with the Minyan; Aruch Hashulchan 422:8
The reason: This is to be done in order so one be able to answer the prayer of Hodu and Ana together with the Chazan. [Admur ibid; See Admur 479:6] Alternatively, it is done in order to be Yotzei the Bracha with the congregation. [Rama ibid; Aruch Hashulchan ibid; Omitted from Admur ibid]
 Admur ibid
 Admur ibid [Mentioned also in Admur 131:5 in parentheses “And even before Davening on occasion one is required to read it, as explained in 488”]; M”A 422:6; Chok Yaakov 488:3; Kol Bo 52; Lechem Chamudos; Kaf Hachaim 422:38
 Shalmei Tzibur 223; Siddur Beis Oved 6; Kaf Hachaim 422:38
 Admur ibid; M”A ibid; Chok Yaakov ibid; Kaf Hachaim 422:38
 This follows those opinions that say a blessing is not recited over Hallel on Rosh Chodesh unless it is recited with a Minyan.
 Implication of Admur ibid; M”A 422:6; Chok Yaakov ibid
The reason: The saying of Hallel during Pesukei Dezimra is not considered an interval being that it consists of Psalms of praise which blend into the Pesukei Dezimra prayers. This is similar to the psalms added to Pesukei Dezimra on Shabbos and Yom Tov. [M”A ibid; Kaf Hachaim 422:38]
 M”A 422:6
The reason: As the blessing of before and after Hallel would be considered an interval between the blessings of Baruch Sheamar and Yishtabach which are already recited in Pesukei Dezimra. Thus, only on Rosh Chodesh and the like in which some Poskim rule a blessing is never recited is one to make an interval and read it without a blessing. [M”A ibid]
 Implication of M”A ibid that the allowance is only within Pesukei Dezimra
 Igros Kodesh 17:67 [See also Igros Kodesh 15:170; 18:81; see Shulchan Menachem 2:250; Shaar Halacha Uminhag 2:175]; See Siddur Admur with glosses of Rav Raskin p. 732 and Hefsek Betefila 5 footnote 6 and Hiskashrus 453:18
 Hiskashrus 748; Rabbi Groner related in the name of the Rebbe, who said in the name of the Rebbe Rayatz, who said in the name of the Rebbe Rashab, that Hallel is not to be said outside of the order of Davening, as Davening Shemoneh Esrei without Hallel is like an old bread that has been baked a long time ago. [Hiskashrus 748]
 Igros Kodesh 17:67 [See also Igros Kodesh 15:170; 18:81; see Shulchan Menachem 2:250; Shaar Halacha Uminhag 2:175]
 See Siddur Raskin ibid that from the letter of the Rebbe ibid it is implied that on Rosh Chodesh the Rabbeim prayed Beyechidus. Vetzaruch Iyun as to the difference