Here is your answer: Yes and this is what is included:
CALIFORNIA BUSINESS AND PROFESSIONS CODE
6067. Oath. Every person on his admission shall take an oath
to support the Constitution of the United States and the
Constitution of the State of California, and faithfully to
discharge the duties of any attorney at law to the best of his
knowledge and ability. A certificate of the oath shall be
indorsed upon his license.
What I really think you are asking about is your situation and that is governed by the contract that you have with the attorney. If you are not happy and they are doing a bad job - then sounds like it might be time to switch attorneys - only you can decide that.
Good luck with your situation.
All CA lawyers are regulated by the State Bar and the Rules of Professional Conduct (linked below), as well as tby he CA Business & Professions Code statutes about what a fee agreement must say.
Sometimes lawyers do charge minimums for phone calls and emails, and family law lawyers often work for a large volume of clients, but this lawyer sounds extremely unresponsive and unfair. I don't see how they can bill you for asking questions they've never even answered.
What does your fee agreement say about calculation of fees? The first place you need to look is that agreement.
Then, ask you lawyer for everything they've failed to provide - every answer to every question, every copy of every document, and an itemization of all accrued fees, and advise them you don't expect to pay for this repeated query for things you're entitled to. If you don't get a satisfactory response, reporting them to the State Bar is an option (linked below). They'll want to avoid that and hopefully will become more responsive to your substantive and billing questions.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
The information provided by Mr. Williamson and Ms. Koslyn is accurate.
It is probably time to stop paying until you get answers.
If you don't seem to be getting any response form the lawyer or the lawyer's office then contact the California State Bar and ask for their help. You can call the State Bar Office of Mandatory Fee Arbitration at 415-538-2020.