(a) Notice of claim shall have been made and served upon the authority within the time limit by and in compliance with section fifty-e of the general municipal law;

(b) It shall appear by and as an allegation in the complaint or moving papers that at least thirty days have elapsed since the service of such notice and that adjustment or payment thereof has been neglected or refused;

(c) The action or special proceeding shall be commenced within one year and ninety days after the happening of the event upon which the claim is based; and

(d) An action against the authority for wrongful death shall be commenced in accordance with the notice of claim and time limitation provisions of title eleven of article nine of this chapter. 2. Wherever a notice of claim is served upon the authority it shall have the right to demand an examination of the claimant relative to the occurrence and extent of the injuries or damages for which claim is made in accordance with the provisions of section fifty-h of the general municipal law. 3. The authority may require any person presenting for settlement an account or claim for any cause whatever against the authority to be sworn before a member, counsel or an attorney, officer or employee of the authority designated for such purpose concerning such account or claim and when so sworn, to answer orally as to any facts relative to such account or claim. The authority shall have power to settle or adjust all claims in favor of or against the authority. 4. The rate of interest to be paid by the authority upon any judgment for which it is liable, other than a judgment on its bonds, shall be the rate prescribed by section five thousand four of the civil practice law and rules. Interest on payments of principal or interest on any bonds in default shall accrue at the rate borne by such bonds from the due date thereof until paid or otherwise satisfied.