Regarding whether animals have souls: although I have found places on the net where people have stated that St. Thomas Aquinas claimed that animals have "material souls," I was not able to find a reference to a writing where he stated this. However, in the Summa Theologica (Prima Pars, Question 75, Article 3: link), he addresses the question of "Whether the souls of brute animals are subsistent?":
"Hence it is clear that the sensitive soul has no 'per se' operation of its own, and that every operation of the sensitive soul belongs to the composite. Wherefore we conclude that as the souls of brute animals have no 'per se' operations they are not subsistent. For the operation of anything follows the mode of its being."
I don't know what the official teaching of the Church is on this topic (which brings up the more general question that is of great interest to me: in general, how does the Summa Theologica influence official Church teaching?).
I did find a site where a priest stated the following:
"Actually the Catholic Church teaches that all living things have some sort of soul, because the soul is the principle of life, the unifying force behind the substance of a being." (link)
However, this doesn't make sense to me - I think in part because his wording seems to me to be inconsistent. He first refers to "living things" but then later to "beings" in general. (A rock is a "being" that has a "unifying force," but I don't think that the Church teaches that it has a soul.)