Saying the Aramaic verses in silent:

The Aramaic part of Kedusha is to be recited privately and not together with another person.[1] It is [thus] not to be recited aloud.[2] [Some Poskim[3] rule that the above requirement to say the Aramaic parts in silent only applies when one is praying together with the Minyan. If, however one is praying is private [or not on pace with the Minyan] then there is no prohibition against saying it aloud.[4] In all cases, the Chazan is not to say it aloud[5], and so was the Rebbe’s custom.]

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[1] Rama 132/1; Zohar

The reason: As the language [i.e. Kedusha] of Targum is never to be said together in unison. [Taz 132/1 and Beis Yosef 59 in name of Zohar]

[2] Rama 132/1; Beis Yosef 59 based on Zohar Parshas Teruma

The reason: Some write the reason it is said silently is so two people don’t end up saying it together. [Beis Yosef 59, brought in Levushei Serud 132; Shalmei Tzibur; Shaareiy Teshuvah 132/2; M”B 132/4] Others say the reason is because the entire establishment of saying it in Targum was for the individuals who don’t understand Hebrew and spoke Aramaic. [Levush, brought in P”M 132 M”Z 1]

Other opinions: The Arizal however was accustomed to read the Aramaic parts aloud. [Shaar Hakavanos p. 49, brought in Shaareiy Teshuvah 132/2, Kaf Hachaim 132/10] Some Poskim question this ruling of Rama being that we don’t hold like the Zohar regarding the Hebrew Kedusha and allow it to be said by a Yachid, and hence the same should apply that we don’t hold of the ruling of the Zohar regarding the Targum. [Perisha 132, brought in P”M 132 M”Z 1] The P”M ibid negates this opinion. Some Poskim rule that the Targum is only required to be said silently if one does not say the Hebrew K3edusha, while if one does than they may both be said aloud. [Piskeiy Teshuvos 132/4 footnote 18 in name of Sefas Emes]

[3] Shalmei Tzibur p. 155 in explanation of Arizal ibid; Shaareiy Teshuvah 132/2; M”B 132/2; Kaf Hachaim 132/10

[4] The reason: As the entire reason for saying it silently is so two people don’t end up saying it together. [Beis Yosef 59, brought in Levushei Serud 132; Shalmei Tzibur; Shaareiy Teshuvah ibid]

[5] Chida in Nitzutzei Oros 5