1: Yes, that matters.
2&3: The bloodline doesn't have enough information to work reliably. The relevant requirement is that you have direct experience of [Natural Pattern Y].
With the given information, you could ask "Is [the reported manner of the diamyo's death] a natural part of [his being assassinated]?"
To which the answer is "yes", regardless of whether he was assassinated or not.
To ask a better question, you would need Y to be "his life", "the current political situation", etc. Which would require that you have direct experience of those things. Note that this still isn't an absolute answer, but it can still reveal surprising truths. For example, if the political situation is unstable but you get the answer "no, it's not a natural part of the local political situation", then that could mean it was a natural death, or it could mean he was assassinated by someone outside the local political situation/for non-political reasons. Similarly, if you get the answer "no, it's not a natural part of his life", that could mean he was assassinated, or it could mean he came under some unnatural stress that made him vulnerable to illness.
4: Yes, the answer is correct even if a human in that situation would not be able to make that deduction. You do need solid premises to start from, though - it needs half-decent priors!
