Halacha Orach Chaim 188

After concluding the Bracha Bonei Berachamav Yerushalayim, Amen is said. The reason for this is to show that this concludes Birchas Hamazon Deoreisa. The Rama says that it should be said softly so that the next Bracha is not viewed as unimportant. However, when Benching with a Mezuman, one should say it out loud.

When reciting the Amen, a short pause should be made before concluding it. The reason for this is to show that the Amen is not part of the Bracha. The Mishna Berura points out in 124,34, that one should not delay too long, or else the Amen cannot be recited, as it will be considered an Amen Yesomeh. We learned about Amen Yesomah earlier.

Since this Bracha is a prayer for mercy and not thanks, like the second Bracha is, Yaaleh Veyavo and Retzei are added during this Bracha on Shabbos and Rosh Chodesh. The addition that comes more often is first, therefore Retzei is recited before Yaaleh Viyavo on Shabbos Rosh Chodesh.

It is interesting to note that the Shagas Aryeh rules that someone who erroneously began Yaaleh Viyavo on Shabbos Rosh Chodesh, should interrupt to recite Retzei, and then go back to Yaaleh Viyavo from the beginning.