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If I get you correctly, your first question is: What is more appropriate, taking the DFT (via the FFT algorithm) of the sum, $$ \text{DFT}\left\{l + r\right\}, $$ or summing the DFTs $$ \text{DFT}\left … $$ Due to the linearity of the DFT (and, hence, the FFT) they are the same $$ \text{DFT}\left\{l + r\right\} = \text{DFT}\left\{l\right\} + \text{DFT}\left\{r\right\}. $$ However, summing $l + r$ in …

The discrete Fourier transform (DFT, of which the FFT is an efficient implementation) is a linear transformation, i.e., $$ a\cdot\text{DFT}\{x\}+b\cdot\text{DFT}\{y\}=\text{DFT}\{a\cdot x+b\cdot y\}. …

The fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT). …

So far I have not experimented with audio steganography, but anyway, maybe these ideas are of some use for you. Adding echoes to a signal is pretty easy as this process just adds a delayed version of …

The choice for the second parameter of the FFT, the FFT length, depends on the specific application. You have to experiment what leads to the best results. …

There exist solutions that are coarsely based on the idea that you propose: Threshold the spectrogram amplitudes to reduce/remove the noise part of the signal. Usually, this will bring about artifacts …