Regarding Kirk's famous yell of "Khan!", I don't think Kirk was faking for Khan's benefit.
Khan is smarter than Kirk and Kirk knows it. But Khan hates Kirk and Kirk knows it, and he knows he can use that to make Khan make mistakes.
Kirk's plan, such as it is, is to keep Khan's attention. Maybe the Enterprise will come to Kirk's rescue, maybe it will just escape, but either of those require that Khan doesn't hunt it down and finish it off. So Kirk separates himself from the Enterprise and makes sure Khan knows.
And Khan's intellect just this once overrides his ego and allows him to decide to deal with Kirk later.
Kirk yells because Khan has decided to ignore him, and that threatens the plan.