part 1) - A straight line on a log-log plot means a simple power law, with the slope giving the power. As the slope is very close to unity, the power is very close to unity. That is, the relationship is approximately linear, or \$I_p \approx kE_e\$. You can try and read the slope very carefully, and write down the power law if you like.
part 2) - There are three potential mechanisms I can think of that might limit the current with increasing irradiance
1) The inherent resistance of the device. As the current increases, the voltage drop across this resistance will work against the photovoltage, and reduce the output. You could estimate this by measuring the diode forward, plotting the result, and extracting the constant resistance at high currents from the log current / voltage relationship at low currents. Or measure the diode output at high flux to simply characterize what happens.
2) I can't think of any physics-based emission saturation mechanism. I suspect the photons interact with the material sufficiently quickly that electrons out = k.photons in, with k being independent of flux, at least up to solar levels. But perhaps some solid-state physicists could correct me on this.
3) Temperature. At some point, with enough incident radiation, the device will heat to damaging levels, and diffusion will destroy the carefully fabricated junctions. Whether you can manage that just by pointing it at the sun, or whether it needs a lens or mirror, you can find out.