As bjlevine attests, Khan was able to sustain some sort of an existence in Ceti Alpha V. The supplies given to him by Kirk were suited for a hospitable environment, but that went out the window when CAVI exploded. Khan had to make do for 14 and a half years. Despite the lack of any scientific probes, he was able to understand the workings of Ceti eels on a person.
He was able to take over the Reliant, and by the Enterprise information given to him (during his convalescence on the vessel), was able to quickly understand Federation starships enough to control (and repair) one with effectiveness. It's possible to assume that if he acquired the data about the Genesis torpedo, he could build one. He was also able to detonate the torpedo (yes, it looked simple, but that doesn't necessarily mean it was simple).
At any rate, his plan to get the torpedo was successful. Unable to find it, he allowed any visitor to the spacelab to discover the device's whereabouts for him (leaving sleeper agents to follow and give the coordinates). Although Kirk was suspicious enough about possible bugging to give a coded message- fooling Khan about the Enterprise's whereabouts and Scotty's talents- once he entered Regulus 1 he was at Khan's mercy. He was unable to stop him from taking the torpedo, and if Terrell hadn't made his fatal refusal, there would be no Kirk for the Enterprise to pick up. With the exception of the Mutara Nebula battle (and even that one had risks like the near collision and Khan throwing his trump card), Kirk had to rely on luck to defeat Khan. Luck that Khan hadn't changed the code. Luck that the Enterprise was able to make any effective shots on Reliant with power on short supply. Luck that Scotty was able to make enough repairs in two hours to enable Enterprise to evade Reliant and engage her for another battle.
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