Answer:
Again, without the context we can't really answer, but I can try to help you.
a. If he changed it to "tiny dead animal" then the meaning of the object would change. By using "tiny dead thing" the reader sees it as an object, but if it's "tiny dead animal" the reader sees it as a creature that was once alive, with feelings and emotions.
b. The connotations with the word "thing" are neutral. It's a bland word that can be used in place of any noun.
c. The word "thing" is a neutral word, and doesn't have deep meaning. The word "invisible" relates to this, because the motorists viewed the rodent as just an object, or a "thing," like it was invisible.