Item Drops and Finds Version 2 - Post BB

i've not tried the pq yet myself (or with a party for that matter), but what from and how often do the alien fragment accessories (and hat, if possible) drop? thanks

I've had stuff drop like every third run or so. The stage 3 midboss and the last boss both drop stuff, but the helm only drop from a special monster that might be summoned when the final boss dies. I've seen it once in 10+ runs, and it didn't drop it.

EDIT: Partly ninja'd.