Before reading your answers:

Problem 2: Given the stated conditions ("you feel strongly that you could never have such biases" is unlikely in my case, but taking it as fact), I would tentatively interpret my roommates remarks as indicating his frustration rather than my disposition. However, I would take the probability of being mistaken as high enough that I would attempt to find some way to defuse the situation that would work either way - most likely, arbitration from a mutually trusted party.

Problem 3: I would quickly review what I know about the debate, and conclude that I have received no additional evidence one way or the other. I would continue to be confident in my naturalist worldview.

After reading your answers:

Problem 2: I notice that you interpret "you feel strongly that you could never have such biases" differently to how I interpret it - I would not feel thus without an observed track record of myself supporting that conclusion. My actions are scarcely changed from those implied by your judgement, however.