Does asuma die?
Yes, Asuma was killed by Hidan; his funeral is in Naruto Shippuden: Episode 77.
I believe that he dies in part 2, during the fight with one of the Akatsuki members, who, I believe to be, Hidan, the more bloodlusty member of the group. Shikamaru does avenge asuma's death, as asuma was his teacher/master/sensei, and he personally kills Hidan, or whoever kills him. Asuma did impregnate kuranai, and she is left to raise him/her by herself, once he dies. He dies in Shippuden. he was curse-killed by Hidan, who is one of the members of the Akatsuki and Kakuzu's immortal partner. Eventually, Shikamaru avenged Asuma's recent death by wrapping Hidan with exploding tags and bury him underground. to make sure noone is to ever dig the rest of Hidan's body parts, the forest where they had their battle was a property of the Nara Clan. Ofcourse, Hidan is still alive, for he IS immortal, but he can't escape because his body was torn apart limb from limb. Kakuzu dies because of Naruto's new elemental jutsu with a combination of the Rasengan.
Correction: He dies in episode 80 and the funeral is on episode 82.