The excitation rate depends on the absorption cross section times the photon flux, assuming no nonlinear effects due to population redistribution.

The excitation is independent of the relaxation (fluorescence) rate, again, assuming no nonlinear effects due to population redistribution.

You need a fairly basic reference, such as

https://www.springer.com/gp/book/9783540734185

What do you mean with excitation "RATE" and what does the unit Hz have to do with it?

The excitation rate is Measured by the generation rate of excitons g on the material with the incident light flux.The generation rate depends on absorption coefficient alpha and the incident photon flux F in photons per cm^2 per second. Specifically the generation rate g= alpha F , where dx is the path length of the photon flux in the material.

Best wishes