hi.... for DIT fft algorithm, refer to this link, it has c-code for that. http://cnx.org/content/m12016/latest/

FT is needed for spectrum analysis, FFT is fast FT meaning it is used to obtain spectrum of a signal quickly, the FFT algorithm inherently is fast algorithm than the conventional FT algorithm

i don’t know

A twiddle factor, in fast Fourier transform (FFT) algorithms, is any of the trigonometric constant coefficients that are multiplied by the data in the course of the algorithm.

because they have a high speed compared to fft