If someone is giving Shiur in the same room as people Davening, do the people learning answer Baruch Hu Uvaruch Shemo and Amen to the Hazarat HaShatz?
Answering to the Shaliach Tzibur is a sign of loyalty to Hashem and the Klal. You affirm that what they are saying is true, and that what they are doing is valid. You even attach yourself to their prayers, benefiting both you and the people praying.
By not responding, you are in effect saying that really you don't care about the klal, and only care about yourself.
Shouldn't be necessary. Better to focus on Talmud Torah.
For those who can't listen to the shiur, you should know that Rav Shlomo Zalman Aurbach rules in Halichot Shelomo 9:6 that one does not even need to stop to answer kaddish or kedusha when learning by oneself, let alone when participating in a shiur!
I once asked a Rov regarding the Halacha of what to do in 770. There is one official Shacharis/Mincha/Maariv minyan ("the main minyan") and there are also side minyanim taking place under the Woman's section throughout the day. Between the "side" minyanim and the "main" Beis Medrash are mechitzos to avoid this issue
However, there are times when people (inappropriately) make their minyan in the "main" Beis Medrash.
My question to him was if I have to answer Amen/Barchu/Kdusha. He said that one really should if possible.
You would have to answer (see Ateret Paz 1:3: Hoshen Mishpat:14:1).
I just looked up the Ateret Paz which Hacham Gabriel cited and he does not say that you have to answer. He brings a citation from Salmat Chaim who ultimately rules that you don't have to answer.