Did Shmuel die now?
Radak: Perhaps he did, after his Nevu'ah was fulfilled in his lifetime, for Sha'ul admitted to David's kingship. He died seven month before Sha'ul (Seder Olam 1 ). For four months and part of the fifth, David was in Sedei Pelishtim (27:7). The episode with Avigayil and David's dwelling in Giv'as ha'Chavilah comprised the remaining two months and a partial month.
Radak: Koheles Rabah 7:4 explained why his death is mentioned here [for the disgrace of Naval. Everyone else was eulogizing and mourning Shmuel, and he made a feast!]
Radak: Perhaps Chazal's source is because the seven months that the Aron was in Sedei Pelishtim are not counted in Shmuel's 52 years, like I explained above (12:2). (Chanah's Tefilah was on the day Eli was appointed. Shmuel was born a year later; after 39 more years the Aron was captured and Eli died. The Aron was in Kiryas Ye'arim for 20 years, until seven years of David's reign in Chevron after Sha'ul died. This leaves 13 years for Shmuel, excluding the seven months that the Aron was in Sedei Pelishtim. We must say that he died seven months before Sha'ul. (Why must we say that all of these years were exact, without extra or missing months? Chazal expounded that Chanah's pregnancy was just over six months (refer to 1:20:1:1), and not a full year! - PF)
Why did David relocate after Shmuel died?
Malbim: As long as Shmuel was alive, he did not reveal that he anointed David, due to fear - "Sha'ul will hear, and kill me!" (16:2) After he died, the matter was revealed via his Talmidim. Therefore, David increased fear of Sha'ul, and while people were still eulogizing Shmuel, David went to Midbar Paran.