Can a retired judge preside over a case without an appointment required by a state statute?

QUESTIONS PRESENTED 1). The XIV Amendment of the United States Constitution guarantees the due process of law. Can a retired judge preside over the case without an appointment required by a state statute? ; 2). The XIV Amendment of the United States Constitution guarantees the due process. Is a case moot if a party voluntarily pays the judgement from the appeal bond under the compulsion of the court order without knowing her rights and without a notice of hearing regarding the appeal bond distribution between the parties? i