The reason why you did not see any spectral lines in the chart on the wall or characteristics in the flame common to all samples that could be attributed to the presence of water and nitrate is because the flame tests specifically measure the spectra of metal ions, not the water or nitrate Ions.
During a flame test, a small amount of the sample is heated in a flame.
The heat excites the metal ions present in the sample, causing them to absorb energy from the flame.
When these excited metal ions return to their ground state, they release this excess energy in the form of light. Each metal ion emits a unique set of wavelengths, forming a characteristic spectrum that can be observed as colored lines. In the case of the samples you mentioned, they contain metal ions that are hydrated (combined with water) and have nitrates as the anion. However, the spectral lines observed in a flame test are primarily due to the metal ions, not the water or nitrate ions. While the presence of water and nitrate may affect the color and intensity of the flame, they do not directly contribute to the observed spectral lines.
To summarize, the absence of spectral lines in the chart or common characteristics in the flame attributed to water and nitrate ions is because the flame test focuses on the metal ions present in the sample, which have their own unique spectral lines.