Are the congregants supposed to stand when responding to the "ברכו" said for the Torah-reading? I've seen varying practices, including a rise-an-inch-from-the-seat-fake-stand.
Depends on your minhag. Some hold that since its a davar shbekedusha you must stand. The Mishna Berurah(146:18) says that even if you wont stand for the krias hatorah in accordance with the opinion of the Maharam M'Rottenberg (quoted by the Rema 146:4) still you must at least stand for borchu for everyone holds you must stand.
The Rama M'pano says the obligation to stand is so much that really one must stand even for the Kria in order not to mistakingly sit during borchu
ולא זע בשעת ברכה משתלי ויתיב גם בשעת ברכו, ועיניך רואות היושבים בשעת קריאת התורה שהן אחד מהם לא קם כדאמרינן טעמא בגמ' מפני הנכנסים והיוצאים, לדברי הכל טוב ויפה לעמוד כל זמן הקריאה דלמא אבל עכשיו שהרבים העולים כלם אומרים ברכו". –
Rav Eliezer Melamed writes:
After the Kaddish,the chazan says, “Barchu et Hashem hamevorach” (“Bless Hashem Who is blessed”). The congregation responds, “Baruch Hashem hamevorach l’olam va’ed” (“Blessed is Hashem, Who is blessed for all eternity”), and the chazan repeats the congregation’s line, saying, “Baruch Hashem hamevorach l’olam va’ed” (Shulchan Aruch 57:1).
The primary purpose of Barchu is to introduce Birkot Keriat Shema,for by declaring “Barchu,” the chazan invites the congregation to recite Birkot Keriat Shema. Even though it can also be recited as praise in itself, like when Barchu is recited at the conclusion of the prayer service, nevertheless, the essence of its establishment was to introduce Birkot Keriat Shema. Therefore, every person must finish saying Pesukei d’Zimrah and Yishtabach before Barchu so that immediately after Barchu he can begin Birkot Keriat Shema. It is best to even skip Az Yashir in order to start Birkot Keriat Shema with the congregation. Still, whoever did not yet succeed in saying the berachah of Yishtabach,even if he already responded to Barchu,must conclude Yishtabach and only afterwards continue with Birkot Keriat Shema.
There are varying customs with regard to standing when responding to Kaddish and Barchu. According to the minhag of most Sephardim,there is no need to stand up while answering matters of sanctity, but one who is already standing must remain that way for Kaddish and Barchu (Maharil,Kaf HaChaim 56:20; 146:20-21; Yechaveh Da’at 3:4). Most Ashkenazim are accustomed to standing while responding to Kaddish and Barchu which are matters of sanctity (Mishnah Berurah 54:7-8; 146:18). However, concerning Barchu which requires a short answer, many Ashkenazim have the custom that if they are already sitting, such as for Torah reading, or before Ma’ariv,they do not completely stand up, rather they only rise slightly from their chairs when responding. This is similar to the custom many people have when answering a zimun with ten men.
When the chazan says the word “Barchu” he bows a bit, and when saying “Hashem” he straightens himself. Regarding the congregation, there are different customs. There are those accustomed to bowing down completely, those who bow slightly, and those who don’t bow at all. Every person should follow his family’s minhag. When people with different minhagim pray together, it is proper that everyone bows slightly (see further in this book chapter 17, note 3).