A minor addendum to that part of my “analysis”.
That statement is only correct for the rooted version of AdAway which only manages the hosts file. There is also a non-rooted version that routes all traffic through a local VPN. I don’t understand how that version works and thus can’t make any statement whether AdAway theoretically could spy on your traffic in that version (the emphasis is on “theoretically” since part C and D in my post are still probably correct)