It shall be the duty of the Council, by continuous study of the problems involved, to devise means to effect the improvement of the administration of justice in and with relation to the county, and to formulate all proper suggestions and recommendations concerning legislation and other measures designed to bring about such improvement. Within the scope of its study shall be the laws of this State relating to judicial organization, criminal law, criminal procedure and civil procedure; all matters relating to the apprehension and prosecution of persons charged with criminal offenses and the penal treatment of persons convicted of such offenses; the functioning of the courts of the county, both internally and in relation to all other public agencies of the State and county whose work connects with that of such courts; the rules of such courts; and the administrative methods employed therein. The suggestions and recommendations resulting from such study shall from time to time be reported in writing to the County Board and, so far as they relate to legislation, shall also be laid before the Judicial Advisory Council of the State of Illinois. The Council shall further co-operate with the Judicial Advisory Council of the State of Illinois in such manner as is or may be prescribed by law in relation to that body.