What is the meaning of "Ni'etz Ni'atzta Es Oyvai"?
Rashi: This is a euphemism (it is not honorable for Hashem to say that you blasphemed Him).
Rashi citing Targum Yonasan: You opened the mouth of the enemies of Hashem's nation 1 . Radak - i.e. they can say that an evil like this was done in Yisrael.
Malbim: [Through your sin,] you caused Oyvei Hashem to blaspheme and anger Him; there is Chilul Hashem in this.
The Targum does not say that Hashem has enemies. Radak (Shoftim 9:13) says that Targum Yonasan distances descriptions from Him.
What is the grammatical form of "Ni'etz"?
Radak: It is Makor (like an infinitive) with a Chirik, like "Chiletz Es ha'Avanim" (Vayikra 14:43).
Malbim: It is Po'el Yotzei (Pi'el); you caused Oyvei Hashem to blaspheme.
Why will the baby die?
Malbim citing Mahari: David always used to debase Oyvei Hashem and disgrace them for such matters, and now he did so. This is like "Hinei Yisarta Rabim" (Iyov 4:3); therefore, he will get another punishment.
Why did he say "You did covertly. I will do in front of Yisrael"?
Malbim citing Avodah Zarah 4b: David was not proper to do that action; it was to show Teshuvah. I.e. it was improper to punish him and reveal the matter in a way that seems that he sinned with an Eshes Ish and through killing Uriyah - which is not true. It was proper to cover up for David 1 , just Hashem wanted to show [the power of] Teshuvah.
One who says that David sinned, he errs (Shabbos 56a). I.e. it was considered a sin only because Hashem is so meticulous with Tzadikim (Daf Al ha'Daf 56a citing R. Y.D. Soloveitzik).
