An increase in dihedral results in a decrease of the total lift produced by the wings. I would like to know the moderate dihedral angle (in degrees) for a low wing airplane, especially the amature built kind( for instance the rv-3).
Also, is there a recommended angle of attack for such category of airplanes.
Please do not worry about the loss in lift. It is real, but so small that it can be neglected. A poor flap or aileron seal will cost you more in L/D than the dihedral ever will.
The loss is proportional to the difference of the cosine of the dihedral angle to unity. With 5° (which is on the upper end of typical values for low wing aircraft) this is just 0.38%.
The exact amount of dihedral depends a lot on details of the configuration:
In general, you need a good balance between $c_{l\beta}$ (dihedral effect) and $c_{n\beta}$ (weathervane effect).
To the angle-of-attack question: It appears you are thinking of airplane design recommendations. In that case, I wonder if you are thinking of wing incidence angle or decalage angle, which are design choices, while angle-of-attack varies as the plane flies.
Wing incidence is the built-in angle between the wing chord and the airplane center line (which in many cases is parallel to the propeller's thrust line). The wing incidence angle, relative to the thrust line, influences what happens when you add or reduce engine power. You normally want a slight positive trim change (nose pitches upwards) when adding power, but not too much.
Decalage is the difference in incidence between the wing and horizontal stabilizer (the wing should always have a larger incidence angle than the stabilizer). A large decalage angle generally makes the airplane more self-stabilizing in pitch, but it also causes larger trim changes when airspeed is increased or reduced.
Angle-of-attack is the angle between the wing chord and the "relative wind" the airplane flies in. It is not set, but varies from slightly negative up to the stall angle of attack, depending on the airplane's airspeed, wing loading, and the lift coefficient of the wing's airfoil. High speed and low wing loading results in a near zero angle-of-attack, even negative for a high-lift type of airfoil, while low speed and high wing loading results in a large angle-of-attack.
The designer normally sets the wing incidence angle so that during normal cruise conditions, which typically imply a wing angle-of-attack of 0-2 degrees, the fuselage sits approximately horizontally, i.e. neither tail low or tail high. In this way the air resistance of the fuselage is minimized during cruise.
Aerobatic airplanes and other agile airplanes typically have a zero-zero setup (both incidence and decalage angles close to zero). This gives high maneouverability and small trim changes as the airspeed changes. The downside is that the stability is low. "The aircraft goes where you point it" and has little inbuilt stability, so it has to be actively flown all the time.
If this sounds complex, it is. Some more on the subject is found at: https://www.av8n.com/how/htm/aoastab.html
