James Kirk: Khan...Khan, you've got Genesis, but you don't have me. You are going to kill me, Khan. You're going to have to come down here. You're going to have to come down here!
Khan: I've done far worse than kill you. I've hurt you. And I wish to go on hurting you. I shall leave you as you left me, as you left her: marooned for all eternity in the center of a dead planet, buried alive! Buried alive!
James Kirk: KHAN! KHAN!
David Marcus: Can I talk to you for a minute?
Captain James Tiberius Kirk: I poured myself a drink. Would you like it?
David Marcus: Lt. Saavik was right. You never have faced death.
Captain James Tiberius Kirk: No, not like this. I haven't faced death. I've cheated death, I tricked my way out of death and patted myself on the back for my ingenuity. I know nothing.
David Marcus: You knew enough to tell Saavik that how we face death is at least as important as how we face life.
Captain James Tiberius Kirk: Just words.
David Marcus: But good words. That's where ideas begin. Maybe you should listen to them. I was wrong about you, and I'm sorry.
Captain James Tiberius Kirk: Is that what you came here to say?
David Marcus: Mainly. And also that I'm proud, very proud too be your son.
[Spock is preparing to enter the radiated warp core.]
Dr. McCoy: Are you out of your Vulcan mind? No human can tolerate the radiation that's in there!
Spock: As you are so fond of observing, doctor, I am not human.
McCoy: Are you out of your Vulcan mind?!
Saavik: You lied!
Spock: I exaggerated.
Chosen answer: I imagine there was a memorial service for everyone killed. Starfleet's policy on corpses is probably to return them to Starfleet HQ where their families can collect them for whatever services or ceremonies they want unless the crewman had left instructions specifying otherwise. There's no telling why Kirk sent Spock's body to Genesis. Based on Sarek's reactions in ST3 he almost certainly went against Spock's wishes, unless of course, Spock left no recorded instructions and Kirk did what he thought would please Spock based on his being highest ranking officer and Spock's closest friend. It also seems very out of character for Spock to just assume that whoever he transferred his katra to would be able to handle it and carry out his wishes (McCoy certainly couldn't!). Ultimately it seems we have to chalk it up to a plot device to base the sequel on.
Grumpy Scot
According to the novelization, Kirk's intentions were to send Spock's remains into the Genesis sun. Lieutenant Saavik altered the trajectory of the torpedo beforehand, due to Spock's desire to see the Genesis effect for himself. The torpedo casing was expected to incinerate when entering the atmosphere. As pointed out by David Marcus in STIII when the pod was detected on the scanners, the gravitational fields were in flux at the time, and the pod had obviously soft-landed on the surface.