On a constant speed propeller, how is blade pitch related to airspeed and efficiency?
A propeller has an optimum AoA, where the thrust/drag ratio is highest. A variable prop can maintain this optimum AoA at a wide range of speeds, thereby reducing fuel consumption. That's all it does.

Fixed wing propellers have a dilemma that at take-off they require maximum thrust, and in high-speed flight the engine will need to be throttled back to prevent overspeeding. Maximum engine power cannot be utilised at every airspeed.


  why is it that if airspeed increases, for a fixed rpm, your blade pitch will increase?


To maintain optimum blade AoA. Increased airspeed causes reduction of blade AoA at constant pitch.


  On takeoff, you want max thrust/power.


You want maximum thrust. This is generated by making the propeller spin as fast as possible (not exceeding tip Mach), with a maximum blade pitch where the blade does not stall. Reducing blade pitch to increase RPM results in no increase in thrust: Power = Thrust * RPM.


  If you increase the blade pitch in these flight regimes, you get a smaller AOA with respect to wind


No a larger AoA. More thrust and more torque on the propeller axis.


  Is it more efficient to give power to blades to move larger loads of air


The engine runs most economically at the RPW where maximum torque is generated, the constant speed propeller speed control wants to maintain that RPM.


  would a blade generate more lift if it had a higher AOA, but at the expense of additional drag on the blade which in turn requires more engine power? Is this drag induced drag because it's an airfoil?


Yes and yes :)