Are mass extinction events more likely during meteor showers / passing through comet debris?
The American Meteor Society FAQ page notes that about 95% of observed meteors are probably of cometary origin. But they're apparently so fragile that they're only about 1/3 of observed fireballs, and 0% of known meteorites.

Also, since the Earth passes through streams of cometary debris several times a year, and yet there's been only one plausible mass extinction due to cometary or asteroid impact in the last few hundred million years (the one that did in the dinosaurs), it appears to be extremely unlikely for cometary debris to be a meaningful danger.