Is it permissible for a Rabbi to deliver a speech or make an appeal in the synagogue once the Torah is placed on the Bima (table), before the Torah reading? Or, does Halacha require a congregation to immediately begin the Torah reading once the scroll is placed on the Bima, rather than delay the reading?
Rav Efrayim Greenblat (contemporary scholar in Memphis) addresses this question in his work Rivevot Efrayim, where he rules that a Rabbi should not, in fact, speak while the Torah is on the Bima. He cites in this context a ruling of the Rema (Rabbi Moshe Isserles, Poland, 1525-1572) in his glosses to the Shulhan Aruch (Orah Haim 147), regarding a situation where two Torah scrolls are used for the reading. The Rema writes that upon the completion of the reading from the first Torah, it should not be taken off the Bima until the second scroll is first placed alongside it on the Bima. The reason, the Rema explains, is that the congregation should not take its mind off the Misva of Torah reading for even a moment. By placing the second scroll before removing the first scroll, the congregation ensures to remain focused upon the Torah reading consistently throughout the entire procedure. This ruling of the Rema demonstrates the importance of remaining focused on the Misva of Torah reading throughout the time that the Torah is outside the Aron (Ark). Hence, Rav Greenblat writes, it is preferable for a Rabbi to speak either before the Torah is removed from the Aron, or after the Torah has been returned to the Aron. He should not speak while the Torah sits on the Bima.
Rav Greenblat further mentions in this context that while the Torah scroll is in the Aron, it is considered to be in a separate domain. As such, the Rabbi may have his back to the Aron as he addresses the congregation, and this does not infringe upon the honor owed to the Torah scrolls. Since they are in a separate domain, the Rabbi is not considered to be turning his back to the Torah. (This ruling is based on a comment by the Taz, Yoreh De'a 282.) Likewise, Rav Greenblat writes, it is, technically speaking, permissible to sit when the doors of the Aron are opened, so long as the Torah has not been removed from the Aron. Since the Torah scrolls are in a separate domain, one is not required to stand. Nevertheless, Rav Greenblat adds, it is customary to stand when the doors of the Aron are opened as an expression of honor to the Torah. (This ruling is based on a comment of the Taz, Yoreh De'a 242:13.)
Summary: A Rabbi should preferably deliver a speech in the synagogue either before the Torah is removed from the Ark, or after it is returned to the Ark, but not while it is on the Bima. When addressing the congregation, the Rabbi may face them with his back to the Ark. It is proper for one to stand when the doors of the Ark are opened, even before the Torah has been removed from the Ark.
