Remember these are wild cats or domestic cats abandoned. They are no Morris type kitties. Cats become territorial and develop colonies. They are loosely matriarchal. A colony of feral cats will not allow just any new member in. There are also disputes over food between feral colonies. When you remove the ability to breed, you eliminate the future of the colony. A single female cat can have a progeny of up to 420000 cats in only 7 years! Eventually over the albeit sad life of the colony, it will eventually die out. If you fail to remove the ability to breed and only relocate or eliminate a colony of feral cats, a new colony will develop from a neighboring colony. There are years of cited history of this occurrence. Google it yourself.
While a domestic cat that lives indoors may reach a life span of 20 years, the typical outside living cat(including ferals) only lives typically 7-10 years. There are exceptions, I, as a child had an outdoor cat that lived to 14, but im not going to split hairs over people trying to help with their own donated time and monies, are you?

Well you know the old saying "ignorance is bliss"
Humans, even those in this country illegally, have many open doors to them to feed themselves. All it takes is the desire to do so. Last i have noticed, there have not been any riots of food shortages.
I am glad that you pointed out some selected Genesis. I am sure you are aware that according to Christian beliefs, God created Man, then animals to keep man company, and then created Eve. i am sure that you realize the same word used in the original Hebrew texts the reference to a Soul was identical for both man and animals. it would appear that God does indeed have us as equals as animals. in addition, God commanded Man to take care of his creation. So i am not sure what your last sentence was getting at, but i would think that a Christian would wish to honor Gods word and follow Jesus' example and heal the suffering.