Standing when the ark is open:
From the letter of the law one is not required to stand when the ark is open, however the custom of the world is to stand out of respect. Nevertheless if it is difficult for one to stand he may be seated.
Standing at the end of each blessing:
In certain years the Rebbe was accustomed to slightly lift himself towards the conclusion of each blessing of Chazaras Hashatz and by the recital of Ukesov and Ubisefer. However in the later years the Rebbe remained sitting throughout the repetition, including the concluding blessings.
Reading along with the Chazan by Chazaras Hashatz:
Although one is required to listen to each word recited by the Chazan in his repetition of the Amidah, nevertheless on Rosh Hashanah the custom in some communities is to read along together with the Chazan. Nevertheless one may not read along louder than the actual Chazan. In however many communities this custom is not followed and they listen silently to the Chazan’s repetition, with exception to the verses of Malchiyos, Zichronos, Shofros of Musaf which some read along silently together with the Chazan. Those that desire to add in their concentration to the words of the Chazan may however read along with him. There is no prohibition in reciting Hashem’s name in these verses as it is like reading verses from the Torah. Those that follow the previous custom may not recite any of Hashem’s names that are part of the prayer. Thus he may not say Elokeinu Velokei Avoseinu, and is rather to start from the word Yimloch.
Q&A on Chazaras Hashatz
Does one have to listen to the entire Chazarah of the Chazan or may he learn Torah or recite Tehillim?
One is to listen to the parts of the repetition that are obligatory and is not to do anything else in the interim. Regarding the Piyutim and verses of Malchiyos, Zichronos and Shofros, it is forbidden for one to learn Torah verbally during this time. This applies even prior to Chazaras Hashatz. One may however think words of any part of Torah without limit. One may even verbally learn matters of Torah that relate to the Tekios. Some also permit one to say Tehillim during this time.
 Taz 242/13; Siddur Yaavetz; P”M 141 M”Z 3; Beir Moshe 1/23; Custom of Rebbe in the early years. In the later years the Rebbe sat. [Otzer Minhagei Chabad 190]
Other opinions: See Panim Meiros 1/74 that one is to stand if he is able to see the Sefer Torah.
 Beir Moshe ibid as there is no requirement from the letter of the law to stand while the ark is open.
 Otzer Minhagei Chabad 190; Hiskashrus 947
 Shaareiy Teshuvah 582/8; Kaf Hachaim 582/59
 Beis David 371 and 378 brought in Shalmei Tzibur 309; Shaareiy Teshuvah ibid; Kaf Hachaim ibid
 Shaareiy Teshuvah ibid; Kaf Hachaim ibid
 Admur 124/6; Minchas Yitzchak 4/48; See ibid and Piskeiy Teshuvos 592/1 regarding the novelty of the Griz of Brisk that one must listen to the parts that invalidate the prayer if they are omitted in order to be Yotzei the Tekios of Musaf. However the Chazon Ish 137/3-5 negates this novelty.
 Har Tzevi 1/42; Piskeiy Teshuvos 592/4; See Minchas Yitzchak ibid and 4/47; as one may not make an interval between the sets of Tekios.
 Minchas Yitzchak 4/48 in explanation of the Leket Yosher from the student of the Terumas Hadeshen p. 128
 Yesod Veshoresh Havoda 11; Piskeiy Teshuvos ibid; however perhaps there he is only referring to Chazaras Hashatz of Shacharis, Vetzaruch Iyun; See however Otzer Minhagei Chabad p. 128 that the Rebbe at times would say Tehillim during the Chazan’s recital of Hineni Heani. Seemingly the reason this is not considered an interval is because it is similar to matters relating to prayer which one may even initially speak of during this time.