Time frames: After both sides have filed all their

Time frames: After both sides have filed all their briefs and had oral argument (or the date for oral argument passes, if everyone waives oral argument), the case is "submitted." If there is no oral argument, the case is submitted at the same time as if it oral argument had taken place. That is why asking for oral argument does not delay the case.
After the case is submitted, the court does not accept any more information about the case. The judges have 90 days from the date the case is submitted to decide the appeal. The clerk of the court will mail you a notice of that decision.