Black plates are best for fluorescence. The curvature of the bottom of the wells usually doesn't matter. I'm not familiar with this particular instrument, so my comments will be general.

If you get the same fluorescence intensity in all wells, no matter what is in them, the question is whether there is no detection of the fluorophore or saturation of the detector. Saturation of the detector would be obvious from the spectra, which would be flat at the top. Since you are seeing a nice peak, you should be able to rule that out.

You can get a signal despite there being no detection of the fluorophore because of the Raman scattering of the solvent. This emission occurs at a specific wavenumber displacement from the excitation wavelength. It can be diagnosed by observing a shift in the emission peak occurring when you shift the excitation wavelength. If that is what you observe, then the problem is a lack of detection of the fluorophore. The concentration may be too low, or its fluorescence may be quenched by something in the solution, or it may have stuck to the plastic surface of the wells, or the selection of wavelengths is incorrect, or the band width (slit width) is set too narrow (if that is adjustable), or the focal point of the light is too high and is missing the sample.

Hi Adam, thanks for your answer it all makes sense. The compound that is formed is fluorescent when using a cuvette and will give a nice emission spectrum. However there is no fluorescence detected using a plate. Any ideas? Same conditions as before.

I already suggested several reasons why the sensitivity may be low in the plate reader. Make sure you select top read, if there is an option for top or bottom read.