There's no actual question and the number of topics covered is really broad in nature, but here's a push start.
1. There's probably libraries that'll help you to do this, or you can use the
Windows Wave IO API[
^] to do it.
2. See 1, that is sampling.
3. If you know the math, do it yourself. Alternatitevly search the net for libraries such as
FFTW[
^].
4. Learn to plot, you can use any of the graphics libraries (GDI, GDI+, etc...).