1)
Why did he mention the king's servants Brachah and David's reaction?
1.
Malbim: Do not say that they did so by themselves, just like Yo'av and Evyasar made Adoniyahu king by themselves. We see that David authorized it!
2)
What was the Brachah to Shlomo?
1.
Malbim: Hashem should aggrandize his name due to his good deeds and Chachmah, and his throne should be aggrandized through great authority. Both will be more than David, for he inherited kingship.
3)
What is the meaning of "he bowed? on the bed"?
1.
Radak: He bowed to Hashem, while on the bed on which he was lying. The same applies to "va'Yishtachu Yisrael Al Rosh ha'Mitah" (Bereishis 47:31).