The blade angle of a fixed-pitch propeller is constant, but the helix angle and the angle of attack will vary according to its forward speed. To ensure its efficient operation the blade angle of attack of a fixed-pitch propeller must be close to the optimum and is that which produces the greatest excess of horizontal lift (thrust) over drag.
The angle of attack of a fixed-pitch propeller increases with increased RPM and/or decreased TAS. Maximum propeller efficiency for any given RPM occurs at only one TAS and the blade angle of attack for that RPM increases with decreased TAS. Therefore, statement 1 is correct.
The purpose of a variable-pitch propeller is to either manually or automatically maintain the optimum angle of attack to maximize the lift/drag ratio of the propeller as the airplane speed changes. This characteristic is the most significant advantage of the constant-speed (fixed RPM) propeller over the fixed-pitch propeller because it is able to maintain maximum efficiency over a range of airplane speeds. Therefore, statement 2 is incorrect.