Do photons exist at all possible wavelengths? My question refers to Photon flux spectrum diagrams. 
The diagram shows the number of photons at different wavelengths. My question is whether the graph is granular or continuous. Do photons exist at all possible wavelengths, or are there some "forbidden" wavelengths?
--- I want to get a PFD data set but not sure how to treat the 0.5 nm increments in the https://www.nrel.gov/grid/solar-resource/spectra.html (G173-03) Spectral data.
Below my calcuations are in green. I am afraid I am double counting photons the way ive done it so far.
(small note the coloumn D should say PFD and not PPFD*)


 A: 
Do photons exist at all possible wavelengths?

Yes. You can essentially treat the background illumination as a full continuum over wavelength, such that any arbitrary wavelength interval, no matter how small, will contain a nonzero amount of energy.
For data sets like the one that underlies the plot in your image, if it is reported at a regular grid in wavelength (i.e. values of photon spectral flux at each wavelength in the list $\lambda_0$, $\lambda_0+\Delta\lambda$, $\lambda_0+2\Delta\lambda$, $\lambda_0+3\Delta\lambda$, $\ldots$), then the standard assumption will be that this represents the integrated spectral photon flux over an interval of length $\Delta\lambda$ around the reported wavelenght, i.e. the reported spectral photon flux at $\lambda_0+n\Delta \lambda$ is the integral of the spectral photon flux over the interval $[\lambda_0+(n-\tfrac12\Delta \lambda),\lambda_0+(n+\tfrac12\Delta \lambda)]$, divided by $\Delta \lambda$.
However, it's always possible that the dataset you're working with is doing something fancier - in which case this will be specified in detail in the dataset's associated documentation.
A: Photons  are quantum entities, they are elementary point particles of energy= $hν$ where h is the Planck constant and $ν$ the frequency of the wave that will be built up when photons of this frequency are accumulated, the emergent classical electromagnetic wave. For single photon behavior see this double slit single photon experiment.. The accumulated interference pattern is a measure of probability distribution of the photons impinging on the double slits.
The wavelength corresponding to  the $ν$ is mathematically within the complex valued wave function of the photon, and can be seen only in probability distributions. As energy has only the limit of conservation of energy, values of frequencies can go from zero to infinity, bounded by the possibility of having an appropriate source, and so do the wavelengths of the emergent classical light beams.
As said in  the comments black body radiation has no limit, except on how probable it is for a very low or very high energy photon to be emitted .
The figure you are describing is a transmission (label  on the right) figure too, so the material interposed will limit by absorption the photon frequencies that can be transmitted.The spectra seen are absorptions from atomic and molecular levels of the transmitter.
