Unless otherwise specified, descriptions are moving left to right and top to bottom. All characters, unless otherwise labelled, were introduced in Kingdom Come (hereafter referred to as KC).
Page 1. Panel 1. The two characters here are Nightstar and Ibn al Xu'ffasch.
Nightstar is the daughter of Nightwing (aka Robin, aka Kingdom Come's Red Robin) and Starfire, from the Teen Titans. The Kingdom Come Revelations supplement says this about her:
Ibn al Xu'ffasch is "heir to the empire of Ra's Al Ghul," who was one of The Batman's greatest enemies and another would-be world-conqueror.
The Revelations supplement says this about Ibn Al Xu'ffasch:
Originally, according to Waid and Ross, Ibn Al Xu'ffasch was tracked down and recruited by Ra Al Ghul's men to run Ra's empire after the latter's death. As we shall see, this piece of backstory has been negated.
Nightstar is wearing the cloak that Ra's al Ghul traditionally wore.
Pages 2-3. The scene here is, of course, the arctic exterior to Superman's Fortress of Solitude, his Arctic (Antarctic and underground, post-Crisis) keep and hideaway. For what it's worth, the surrounding environment is depicted somewhat differently here than in KC.
Page 5. The stashing of the remains of this individual were mentioned in KC #3, page 13 (page 123 in the collected edition). How Ibn al Xu'ffasch would have known this is, of course, another issue.
Page 6. Panel 1. The character seen here is Brainiac, in a new configuration. Brainiac, an alien robot, has always been one of Superman's deadliest enemies, and was responsible for shrinking the city of Kandor, the former capital of Krypton. The Silver Age Brainiac was a green-skinned android with a design of wiring on his forehead very similar to the four-pronged wiring seen here.
Panel 4. The remains seen here are of Superman's "super-robots," who during the Golden Age (and presumably today, in current DC continuity) were used by Superman to help him fight crime and take care of the Fortress of Solitude.
Page 7. Panel 1. Ibn's "grandfather" was Ra's al-Ghul, who was one of the Batman's greatest foes, a criminal genius and the head of a worldwide criminal organization.
Ra's' "Lazarus Pit" was used by Ra's to renew his energies and, in some cases, bring him to life. Panel 3. "Ra's al Ghul" means, in Arabic, "the demon head."
Page 8. Panel 3. As Mark Coale points out, Batman keeps the heart of Ra's in a trophy case? Huh?
Page 9. Mark Coale notes that Brainiac has lost his hair between page 8 and page 9.
Page 11. Panel 3. Ra's daughter is Talia, who in DC Continuity has long been attracted to Batman, and he to her, but because of their respective positions the love could not be consummated. In the Son of the Demon the did consummate the relationship, but post-Zero Hour the graphic novel, and Ibn al Xu'ffasch's existence, are no longer in continuity.
Page 12. Panel 2. This is the Batcave as shown in KC, with the Bat-Knights (robots that Batman used to fight crime in Gotham City).
Page 13. Panel 2. This scene is from KC #4, page 40 (page 198 in the collected edition), symbolising a reconciliation between Dick Grayson and Bruce Wayne, and Nightstar and Dick Grayson.
Panel 3. This scene is from KC #4, page 39 (page 197 in the collected edition).
Panel 4. The "little death" is, of course, poetic for the orgasm.
Page 14. Panel 1. The "temper" referred to here is explained somewhat more fully in panel 3: the impulses and temper of Nightstar's mother, the Tamaranian Starfire, an intemperate member of an intemperate race.
Thanks to Mark Coale, as usual.