1)
Why is he Chayav Misah?
1.
Rashi: One who steals from the poor is Chayav Misah [bi'Ydei Shamayim] - "Es Nefesh Ba'alav Yikach" (Mishlei 1:19).
2.
Radak (1): This is an exaggeration. He is not Chayav Misah. He said so because he did something repulsive.
3.
Malbim: Judges judge according to Torah law, based on the action. One who steals and slaughters a sheep pays four-fold. A king judges according to the [need of the] time and the doer. His cruelty and evil heart are worthy of death. Nasan asked David to judge him like a king!