Legal Question in Civil Litigation in California

1) Assuming your mother served the lawsuit and there is opposing counsel, the Judge should have asked opposing counsel to be there, as well. If the lawsuit has not been served, your mother is the only party to talk to.

2) No.

Sounds like you ARE acting like an attorney for her. No wonder the judge was angry.

The judge can order a hearing continued to a different day. It doesn't have to be the next day, but it can be. That's probably what happened here.

Parties are usually required to give advance notice to the court and to each other when they file motions. Courts are not bound by the same rules.

The fact that you were translating for your mother does not mean you weren't also acting as her advocate. A translator is only supposed to translate and, where needed, ask for clarification. If you inserted your own ideas into the proceeding then you crossed a line. Since I don't know what was said, I can't say whether you acted improperly or how serious any violation might have been.