Though we do not have a cat in our household due to having an anxious dog, we have several neighborhood cats that like to sun themselves in our yard. Do you have any cats?
No, I don't have cats either.  I'm allergic, but I am intrigued by the species and their ability to hunt and catch vermin so easily.  
Exactly, that is why I never chase them off. Ever since the cats have been around, I have not had a single issue with mice in the house.
I agree.  They hang out in my backyard and I believe it helps a lot.  They hear sound too faint or too high for the human ear like those made by mice and rats.
And also a growling dogs. My terrier does not like that they are in her space but they have grown accustomed to a bark or two.
That's so funny.  Cats are really smart and prefer to be solitary hunters.  So I'm sure the cat doesn't like your dog being in her space as well:)