What is the reason for the blue color of an ammoniated electron?
Both of your questions could benefit from more background, so please forgive me if I understood something wrong. However, I'll try to answer as best I can:


The excess electron in liquid ammonia is not really independent, otherwise, as you stated correctly, the electron would not absorb a certain wavelength but act as a black radiator/absorber like in a plasma (for example the sun). However, how the electron is bound and how the transitional states are formed is not completely understood yet. In this paper, I found the following sentence: "The excess electron in liquid ammonia ("ammoniated electron") is commonly viewed as a cavity electron in which the s-type wave function fills the interstitial void between 6 and 9 ammonia molecules." And then they go on to present a different hypothesis...
In a flame, the spectrum is recorded in the gas phase and formed not by the salt but by the individual atoms (even if you put the salt into the flame). Thus the spectrum depends only on the elements contained in the salt, not on the type of salt. This is different, if the spectroscopy is performed in the liquid phase of alkali metal halides. There the spectrum depends on the mole ratio of the anions and cations.