With respect to all, Khan obviously did not know what Genesis' true function was...save for whatever information he could pry from Chekov, Terrell, and other knowlegeable members of Reliant's crew. And at that, all he could probably get was that it was some kind of terraforming device, but they did not know the mechanics behind it. That is a bonus part of the explanation as to why Chekov and Terrell ended up on Ceti Alpha V, and not Ceti Alpha VI as they previously thought. (The Ceti Alpha system must've really been an obscure and disinteresting system for them not to have noticed that the place was missing an entire planet.

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Khan didn't know anything about the Genesis build team...especially did not know that the device's co-creators were mother and son, and connected to Kirk. Using Kirk as a scapegoat for Reliant's sudden move to "appropriate" the device from the scientists on Regula was more of a happy accident. The "who's who" of all this was probably not important to Khan. He simply used Kirk's name and position as Chief of Starfleet Operations to force Regula I's compliance. (At least, I think he's still CoSO at this time....Regula certainly had no reason to listen to the Chief of Starfleet Training Command, or the Commandant of Starfleet Academy.). Khan simply banks on the notion that Kirk will do what he must to protect crew, personnel, and assets, and would be more induced to see to the matter personally now that his name has been invoked. Khan doesn't realize, and I don't think he ever learns Kirk's relationship to the project leaders. (Certainly Kirk didn't realize his full relationship to the male project leader until he subdued David, and laid eyes on him, then hearing Carol come running frantically to the scene....but I digress

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So, Khan sets course for Regula I spacelab He cannot access any information to Project: Genesis. It was information that was likely not needed aboard Reliant...or to be accessed via subspace via Reliant's command contingent. He figures the only way to get that information was to go there himself and prise it from the build team. He comes away from the spacelab empty handed, not counting on the stalwart nature of the teammembers left behind to protect Drs. Marcus' whereabouts and/or involvement. He had tortured the stragglers to death. Then he had to get back to Reliant to blow Kirk to bits, knowing full well that Kirk must be on his way by now. (Or Mr. Kyle informed him that the Enterprise had been dispatched, under the command of Kirk)
Khan, in the attack on the Enterprise, presses Kirk for the information. Kirk feigns ignorance, which Khan doesn't buy for a moment. Kirk stalls for time and routs Khan, just barely. Khan, once again comes away, twice as empty handed. No info on Genesis, and no revenge on Kirk.
In time, he pursues Kirk to the only logical place for him to go....Regula I. In his sagacity, he left Terrell and Chekov behind at the spacelab, in case Kirk got past Khan, to carry out the final revenge, should Khan not be able to make it.
Khan arrives, by happy accident, at the right time to listen in as Terrell broadcasts their location to Khan, and confirms that they are in the presence of the Genesis device. After a bit of mayhem, and some prodding by Kirk, Khan has the device beamed aboard, still none the more intelligent about its true purposes. During the time when we see Kirk, McCoy, Carol, Saavik, Chekov, and David have their pow wows and revelations inside the Regula moon, Khan has probably had time to at least look over the device, and if he used theoretcial tech application to divine anything about the device, he discovers it is some kind of delayed explosive, possibly of an incalculable (to him, anyway) order of magnitude, if it's meant for purposes he vaguely gleaned from Reliant's crew. By it's looks, it could be deployed as a torpedo, a mine, or a planted bomb. Banking on the notion that it is a high order explosive, he keeps it as his "ace in the hole" against Kirk, if he cannot destroy Kirk by conventional means, and is probably about to near mortality himself.
In summation, I really don't think Khan knew Genesis' full potential. He gave up his plans on conquest when he lost those nearest and dearest to him...namely his wife, and devoted his life solely to revenge against James T. Kirk. He didn't care who stood in his way. He didn't care how he did it, or what he had to use to do it.
Personal opinions only. And remember, they are ONLY opinions.
