There are obviously a lot of questions here.  First, as a director you are entitled to see the ED’s contract.  The board’s selection and continuing evaluation of the ED is one of its most important responsibilities.  If her contract is up for review, it is not micro managing to understand its terms and to have the board, or at least a committee of the board, evaluate her performance. You should be setting annual goals with her for her performance and doing an annual performance review.

It is not unusual for an ED to be in charge of hiring staff for the organization, but this is also something that should be set out in her job description and your other policies.  If you are expanding the operations, it may make sense to hire a new associate.  You should have an annual budget based on the anticipated staffing level and salaries.  Going significantly beyond the budget would normally warrant getting board approval.

She appears to have done good things for the organization, but I am concerned about her bullying and lying. Your evaluation committee ought to be talking to her about that, and if you do retain her, you ought to make clear that such behavior has to stop.  You may be willing to live with some bad behavior if she is really a genius.  You can refuse to react to her bullying.  But you can’t live very well with lying.