You are actually writing about two motions: 1) a motion to continue trial date; 2) a motion to reopen discovery.
With respect to your questions regarding the motion to re-open discovery and the meet and confer requirement the reason is that, if all other parties agree, it would not be necessary to obtain a court order. The parties would simply conduct the discovery.
If a motion to re-open discovery is necessary because the other parties will not agree to the additional discovery you must file a formal motion consisting of a notice of motion and motion, points and authorities, and a declaration showing good cause. You must fully discuss items 1-4 of Code of Civil Procedure 2024.050(b) in both your P&As and declaration.
Yes, a court appearance is required and you must timely serve all other parties with a copy of your motion. Remember you cannot sign the proof of service yourself.
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