I'm not certain that I can provide the answers for your story, but I can describe how I would choose to address them. I usually spend time writing back stories for the main characters. I'd start with the AI.
I'm a little confused as to whether the AI is the sole inhabitant of the ship or not. What was its primary mission? I'm not certain what "racial ennui" might be and why the AI would desire to overcome it and why it feels that some other, biological being is needed to accomplish the task. It appears that Earth is an unexpected find, so human culture would likely be unknown to the AI. This would imply the questions might be naive and driven more by what culture the AI does know, the woodland creatures (and the now deceased crew?).
If the AI's knowledgebase is driven by its interactions with the woodland creatures, then their culture will be the driving force behind the AI's questions. If the AI's goal is to overcome racial ennui, then I suspect it would question the human contact about characteristics indicating it and what are alternative human feelings in that regard. Also, the questions should reflect the woodland creatures' nature as understood by the AI. Are they passive and skittish? Are they territorial and aggressive? Are they well suited to survive when dropped onto some new planet? What are the characteristics of this new planet, which are implied to be different from Earth's and human's? Why would human knowledge be beneficial? The question set would like be driven by the information that the woodland creatures would need.
Lastly, would there be a selection process? If no one on Earth knows of the existence of the ship, how would the AI interview people? Would it be more of a case of the ship being found at random? What are the consequences of a random individual failing the AI's question test?
For me, I usually like to understand what drives characters to arrive at the start of the story. With that in mind, I find it is easier to make decisions on what they will do in various situations.