DFT Fourier, lengh an cosine

First merry christmas to all


Question: DFT length

1.Does the lenght N
of the DFT input signal need to be the periodic lenght with x[n]=x[n+N] to to give the right output signal?
I mean if I have a quantisized signal, with many many points, then I have first to find the right lenght N by checking x[n]=x[n+N], right? Hand by hand, or how do I do it?


2. Is the output of the DFT (always) based on the cosine function (no matter what the input is)? I mean, the DFT of sine is c=0−i∗1
wich means −90° phase shift, so sine = cosine(-90°)

thanks