1)
Did David believe the Leshon ha'Ra that Tziva said about Mefivoshes?
1.
Malbim (3, like Rav, Shabbos 56a): Yes. He was punished, and immediately after this Shim'i ben Gera cursed him.
2.
Shmuel (Shabbos 56a): He did not believe it. He only suspected it. The gift was on condition that his words will be found to be true.
