Answer to Question 1
It is so hot that almost all the energy it gives off, by Wien's Law, is not going to be in the visible, but the X-ray portion of the spectrum. Also, it is very low density, so there are far more atoms at 5,800 K giving off a lot of visible light than the few out in the corona.
Answer to Question 2
Amplitudes of sound (and water) waves can differ greatly and still have the same wavelength and frequency, as they are the result of the motions of large numbers of molecules. For photons, the energy is quantized, so that each photon of a given wavelength must carry the same amount of energy.