My anime question stands on this too. It would make more sense knowing some of the characters, for example:
With your first question, her collar is a joke between her and her gang. Not really her gang but her friend that shares the same sin. Do to her canine looks already: Wolf ears and tail. Her friend, Greed puts a dog collar on his dog "chimera" Dorochet and on Avarice. So just to please him she continues to wear it, and actually begins to like it.
All the tag says is her name. Let me just say she about kills Greed to at least take off: "Property of Greed" "If found return her to the Devil's Nest"