I have the Fourier transform $S(\nu)$. If I oversample by a factor $R$ in the frequency domain. Does the duration of the signal $s(t)=IFFT(S(\nu))$ change?
Oversampling a spectrum is a non-linear process. Specifically, since each bin is suppose to represent an integral number waves in the sampling window, oversampling must be done in accordance with that. But to answer your question, and assuming the spectrum is of some finite time domain window, the new time domain window duration is the wavelength of the lowest frequency bin in the FFT.