Hearing on a noticed motion has been continued by the Court, is the time for filing oppositions and replies, likewise extended?

The time for filing of oppositions and replies is determined by the date of the continued hearing, not the initial hearing date (as long as the opposition or reply date had not already passed before the hearing was continued). Reply briefs are due to be filed no later than five court days before the hearing and must be served in a manner which is reasonably calculated to ensure delivery to the other party or parties not later than the close of the next business day after the time the reply papers are filed. See Code of Civil Procedure Section 1005.