(a) The board shall have the power and duty to:

(1) Provide for the collection of all moneys;

(2) Provide for the payment of all administrative expenses;

(3) Hear and decide all applications for retirement benefits under this chapter;

(4) Provide for the payment of all retirement benefits that may be determined to be due under this chapter and lawful rules and regulations as adopted by the board;

(5) Make all necessary rules and regulations not inconsistent with law for the operation of the fund;

(6) Determine and fix rules of eligibility for retirement benefits under this chapter; and

(7) Provide for refunds and repayments to persons who may be entitled to receive them.

(b) The board shall have all other powers necessary for the proper administration of the fund.