Welcome to PhotoStructure, @hitmonchancoco !
Yes. Details about “automatic organization” are here: https://photostructure.com/getting-started/automatic-library-organization/#what-happens-when-you-choose-yes
Not currently, but I’m building that today (yay!): deleting and hiding is the most voted-for feature request.
A bare-bones implementation should be available in a beta in a couple days.