This time, Omega asks you to consider the counterfactual world in which the device still shows "Working" after 5 minutes. Should counter-factual Omega still write "Even" on the test?

It should write whatever you would write if you observed no answer, in this case we have indifference between the answers (betting with confidence 50%).

In a different Omega-suggested counterfactual world, a black swan flies in the window after 4 1/2 minutes and the display shows "Disproven". You know that this means that either a). Arithmetic is inconsistent. b). The theorem prover device is unreliable. or c). Omega is messing with you.

If device is unreliable, it's unreliable in your own event in the same sense, so your answer could be wrong (as improbably), so the original solution stands (i.e. you write "odd" in the counterfactual). Even if Omega proves to you that arithmetic is inconsistent, this won't cause you to abandon morality, just to change the way you use arithmetic. Omega is not lying by problem statement.

And subjective probabilities cannot flow backward in time (surviving the erasure of the evidence that produced those subjective probabilities). Even Omega cannot mediate this kind of paradoxical information flow.

We discussed in the other thread how your description of this idea doesn't make sense to me. I have no idea what your statement means, so can't rule whether I disagree with it, but certainly I can't agree with what I don't understand.