What are the flight rules for crop dusters?
14 CFR Part 137 regulates agricultural aircraft operations, with §137.51 discussing operation over congested areas, including:


  The crop duster must operate “with maximum safety to persons and
  property on the surface” and the crop duster must have obtained prior
  written approval from the FAA and notice of the intended operation
  must be given to the public. Further, the crop duster must submit a
  plan to the FAA that considers the flight obstructions and plans for a
  possible emergency landing.


Of utmost importance is the section regarding the flying of restricted category civil aircraft such as agricultural aircraft:


  Sec. 91.313 — Restricted category civil aircraft: Operating limitations.
  
  (a) No person may operate a restricted category civil aircraft— (1)
  For other than the special purpose for which it is certificated; or
  
  (2) In an operation other than one necessary to accomplish the work
  activity directly associated with that special purpose.
  
  ...
  
  (e) Except when operating in accordance with the terms and conditions
  of a certificate of waiver or special operating limitations issued by
  the Administrator, no person may operate a restricted category civil
  aircraft within the United States—
  
  (1) Over a densely populated area;
  
  (2) In a congested airway; or
  
  (3) Near a busy airport where passenger transport operations are
  conducted.
  
  ...


More information is available in this FAA document.