Short answers, pulled from the story.
Liquid Snake led the Shadow Moses Island operation on the 18th of September 1995. This hostile takeover was a desperate attempt to harvest Big Boss's remains to cure genetic mutations plaguing his Genome Soldiers.
Liquid Snake believed Solid Snake had superior genes due to a cruel misunderstanding that Solid inherited the superior DNA while Liquid was left with flawed ones. In reality, Liquid carried the superior genetic code of Big Boss while Solid was the inferior copy.
Liquid Snake survived the destruction of Metal Gear REX by engaging in a brutal fistfight atop the ruins before escaping in a high-speed jeep chase. The chase ended in a crash outside the facility where Liquid succumbed to the FOXDIE virus.
Liquid Snake's right arm was transplanted into Revolver Ocelot, creating a vessel that carried Liquid's voice and mannerisms. This surgical integration allowed Liquid's personality to resurface whenever Solid Snake was nearby.
Eli was a twelve-year-old child soldier who existed before Liquid Snake and fled his home in England after learning the truth about his nature as a clone. He established a mercenary unit on the Angola-Zaire border known as the White Mamba.
Eli died after a battle between Sahelanthropus and a battalion of Diamond Dogs soldiers where he lost his immunity to the vocal cord parasite during puberty. The Third Child used psychic powers to remove the parasite within him before escaping as Diamond Dogs launched a Napalm airstrike.