Most commission contracts do not = work for hire. This is a specific legal doctrine. The written agreement would include assignment language.
Model releases are part of the right of publicity piece. This is not a part of copyright law and can vary greatly from state to state. And it applies to people, not animals.
Fair use doesn’t apply to the person that owns the copyright. There’s basically no commercial use that qualifies as fair use. The copyright owner (photographer) can make whatever use they want so long as not otherwise illegal (like child porn or something).
I do this for a living and have a specialized advanced degree in this area of the law.