As with so many questions in the nonprofit world, there is no single answer to either of these questions.

Many people serve on more than one board of directors at the same time.  It is not likely to be a substantive conflict if the organizations are not “competitors” in providing similar goods or services.  It may create a conflict if both organizations expect the directors to solicit their friends for contributions.  These issues can usually be worked out.  The more significant issue, especially if the individual serves on a bunch of boards at the same time, may be whether the person will have the time to devote to your organization to fulfill the roles and responsibilities you have spelled out for directors.  If the person can’t make the commitment, or fails to meet the commitment, you might want to ask for help elsewhere.

What happens to daily operations when the executive director leaves largely depends on the size of the organization.  If there is little or no other staff, the board may have to provide services directly to keep the organization functioning.  With a larger organization, a director could serve temporarily as CEO until a new executive director is found.  Organizations ought to have succession plans, particularly emergency succession plans, in place so they know in advance how they will deal with the loss of the chief exec.  A knowledgeable board member may be the best choice to fill in on a temporary basis.