If, say, a quarter of people are murdered by their roommates, and males are 10x more likely to be killers than females, what's the odds of a female roommate doing it?

Depends on whether murder by roommate and murder by female are independent. An average taken over the all homicides includes gang violence, robberies, bar fights, etc. Some kinds of murders are overwhelmingly perpetrated by males, while others are more balanced (for example, males are only 50% more likely to kill their children than females). Once we narrow down the circumstances of the murder, all kinds of dependencies and conditionals start popping up and the base rate becomes less relevant.

A probability like 2.5% is worth following up on if police have no better leads to focus on, but they visibly focused on it way more, and in fact people focused on it way more; consider how many expressed probabilities were higher than that in the LW survey.

Agreed. Police try to shoehorn in their theory and the press isn't going to let the truth get in the way of a good story.