To me, there doesn’t seem to be a very big concern over Learning or Gathering Information. I did not get the sense that Understanding was constantly addressed either from the characters throughout the film.
Now there is a bit of Obtaining in the mix, Carol Marcus definitely wants Genesis back, Kirk wants to get it at some point as well, Khan obtains it midway through but the nature of the goal didn’t feel to me as though the device was at the center of everything.
Khan was Doing things since the very beginning to attract Kirk, causing problems for The Federation. He mind controlled some of members of the Federation to deceive the scientists in charge of Genesis (Carol Marcus). He steals the Genesis device. Kirk tries to deceive Khan and gets his own ship damaged. Khan leads his crew into the nebula which ends up being his undoing.
Kirk - How Things Are Changing - Maybe at one point he was able to convince himself of a no win situation but now he must face the idea that that isn’t always the case. Throughout the film he’s trying to cope with the fact that he is getting old and worn out.
Spock - Impulsive Responses - The only thing I can think of here is that his selfless act to get warp drive back online got him to think of Spock in a different light. To reflect back on his wise words and get him to feel young again.
Relationship - Manipulation - There were many instances where Spock was trying to relay some very inspiring words to Kirk to get him to realize his true role of Captain which would get Kirk out of his slump both personally and professionally. It finally worked when he sacrificed himself to save the Enterprise.