Why did ADVENT kill all domesticated animals?
Most often extraterrestrials are identified and alerted to owners by domesticated animals, like dogs, cats, parrots, etc.
Since Advent has actually become a surrounding of people but in a way to sway their alertness, it sounds as normal act to prohibit anything that would go against them or serve as base for rejection.
Feeding species with its own remains (in any form) has proven to be overly bad idea, for example mad cow diseases, and I would expect the same for humans (let's not go into topic of cannibalism yet). Except if broken down to prebiotic soup and syntethizing something from that.
I think is a sort of joke or easter egg and an interesting idea:
Easter egg: in old XCOM UFO game when you entered alien spaceships on missions, in larger ships you could see lots of horses and cows being abducted and in operation tables and so on. Maybe they imply that they just abducted all of them.
Interesting idea: since ADVENT has been trying to control mankind in subtle ways, and it has also been said that they for instance make hamburgers from human flesh from their human farms of sorts, it makes sense that they want to change the whole ecosystem to really depend on human farming and actually adapt the planet for that. It seems human can be feed with human and that's all you need to support as alien farmer... Doesn't sound as a good plan, but hey...
The question about how they manage to kill all cows and pets remains though.