If I pay a photographer for services, the photographer owns the copyright unless we agree otherwise in a contract. If there is no agreement, the creator owns the work.
My (very limited) understanding is that the rule about works for hire only applies to non-employee contractors under certain tightly defined circumstances. Actually employing a photographer as an employee would mean you own the copyright, paying the photographer as a contractor would not.
Depends on the jurisdiction. Where I live, the employer has an implicit exclusive license to the IP produced by their employees. In theory, employees can even rescind that license but will need to compensate the business (in practice I don't think that's actually possible, the monetary damages to the employer would be ridiculous).