Frequency detection in audio and what parameter or set of parameters help/limit frequency detection
I'll give a few answers with the qualification that this isn't really my specialty area:

1) If you are using a DFT (FFT), then you should keep your sample frames relatively short.  Speech utterances are of short duration and the DFT is best with steady tones across the entire frame.

2) Your sampling rate will likely be 44.1kHz (CD quality) or 8kHz, either of which is sufficient that the Nyquist frequency is nowhere close to the ranges you are talking about.  In other words, this shouldn't be a concern.

3) Music tones tend to be of longer duration and a bit steadier.  But long drawn out vowels fit the same pattern.

My advice would be get some software, like Audacity, that has a good spectrogram function and look at speech and music samples that way.  Or write your own.  Anyway, that is a good starting point to build up some familiarity with what various sounds and voices look like in the frequency domain.