Legal Question in Construction Law in California

First, question #2. The California Supreme Court will not accept a case that was dismissed at the Court of Appeal level for a routine failure to adhere to schedules.

As to #1, I think the next step is to retain a lawyer that (a) knows how to get relief from the order of dismissal at the Court of Appeal, and (b) can get papers filed on time.

The Court of Appeal doesn't care what kind of violations are involved in your case. Most cases are about some kind of violation of rights. Further, it won't know what your case is about until all the papers are filed. Cases are reviewed in the Court of Appeal when all the trial court records and all the parties' briefs are before it, and not sooner (at least not usually).

The Rules of Court setting the time line for filing Appellant's Opening Brief are 8.212 and 8.220, the latter covering the effect of failure to file a brief. Note that there are provisions for a grace period and for requesting additional time before the grace period expires. However, I understand that the only way to reinstate an appeal once the Court has entered an order of dismissal is to prepare, file and serve a motion to vacate the order of dismissal. Such a motion lies under Code of Civil Procedure section 473(b)

A motion to vacate should be made promptly, because the Court of Appeal likely will soon issue a "remittitur" returning jurisdiction to the trial court, and after that happens there must also be a motion to recall the remittitur.