Whether an elected judge must personally take the oath of office and sign the document in the presence of the administering officer, and if not, does this constitute judicial fraud or disqualification

(1) Does an elected judge must take the oath of office? (2) If yes, then must that judge sign the document in the present of the officer who administer the oath? (3) If that judge didn't sign the document, could she still be considered she took theoath of office? (4) Can an elected judge have someone else take the oath of office for her? (5) If the answer is no, could it be said that that judge took possession of the court through means of fraudulence if she entered the duties of that court .. without taking the oath of office? (6) Would that judge be disqualified if she enter upon the duties of the court without first taken the oath of office? (7) Does judge's qualification and jurisdiction of the court be subjected to the ~ AEDPA imposed 1-year limitation, or could it be challenged at any time? (8) When the jurisdiction of court being challenged, does court be permit to ignor the issue or the issue must be resolved?