To answer your questions:
1. An incompressible-ideal gas law is used to estimate the density of an INCOMPRESSIBLE fluid using the ideal gas law (check out section 7.3.6., Fluent User's Guide).
2. The density drop down in the material property panel allows you to choose the Boussinesq approximation model and it uses a constant value of density by writing the buoyancy term as a function of operating temperature (section 126.96.36.199, Fluent User's Guide). You will also have to specify thermal expansion coefficient (beta).
3. Operating density is non-zero because it appears in the body-force term of the momentum equation. When Boussinesq approximation is used, this value becomes irrelevant and therefore need not be specified. Care should be taken while specifying the operating density (section 188.8.131.52, Fluent User's Guide).
I hope this helps.