1)
Why does it say that Nasan went home?
1.
Radak #1: He left immediately after saying the Nevu'ah. He did not honor him to continue to sit with him, to show that there was anger [from Hashem] against him.
2.
Radak #2: Immediately after Nasan left, Hashem struck the baby.
2)
Why does it say "Asher Yaldah Eshes Uriyah"?
1.
Malbim: Hashem considered her to be Uriyah's wife. (This is why He struck the baby.)
3)
What is the meaning of "va'Ye'anesh"?
1.
Rashi: He became ill.
2.
Radak: He became severely ill. This is like "Anushah Makoseha" (Michah 1:9)