Why only take 205 sample when using a sample rate of 10khz or 8khz?
The frequency of DFT bin centers is i*Fs/N, for integer i.  Thus different N will create different arrays of frequencies.  For some N, this will produce an array that has the lowest nearest bin center distance from the frequency set that you wish to measure (in thus case, a vector of DFT frequencies).  According to the referenced document, for some standard sample rate, N=205 will produce that vector with the closest DFT bin centers to DFT frequencies.

Since each DFT bin has a Sinc shaped roll-off, the closer a bin frequency is to a desired measurement frequency, the lower the magnitude measurement error will be without needing further interpolation computation.

For N greater than 320, the DFT will have greater frequency resolution, but the time resolution gets worse and will overlap multiple tones, which creates greater ambiguity in which tone is being detected.