Trivia: Kriste Alley turned down the role of Savvik in star trek 3 & 4 for fear of being typecast.
Trivia: In 1983 this movie held the record for all-time best-selling home video release, largely owing to a then-bargain $39 price point. In the early 80s most movies on tape were priced around $70; the belief was that only enthusiasts and high-end customers were interested in owning movies and most people were satisfied renting. The stellar sales of Star Trek II proved there was a mass market for home video sales and the entire industry shifted in response.
Trivia: Early storyline development used essentially the setup for the Star Wars films only the villain was on the side of the rebellion. David was a (villainous, initially) version of Luke and it was a plot twist that Kirk is his father. The Genesis device was a planet-destroying weapon a la the Death Star, Khan lurked in the shadows dressed in a cloak and used psychic powers like the Emperor, and Spock would have died in the middle and at the end speak from beyond the grave like Obi Wan Kenobi.
Trivia: Khan says to Chekhov and Terrell, "I never forget a face," referring to Chekhov. But, Chekhov was not a member of the original cast of Star Trek at the time the Botany Bay was discovered in space, with no evidence Chekhov was meant to be in the crew already. So, Khan had never seen Chekhov's face for the first time until that moment on Star Trek II.
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.