Legal Question in Criminal Law in California

Your question is impossible to answer as presented. It depends on the type of board you're talking about. A private company's board of directors, would generally have policies regarding felons that may prevent it. However, if you are asking about some general law that prevents someone from serving as a director on any board of directors simply because they were convicted of a felony, the answer would be no. A felon could serve as a director on a board of directors. The conviction should not preclude them from serving on the board.

Yes, subject to the company by laws and restrictions. Read them.