Fourier transform of a periodic/aperiodic signal Generally speaking, I know that periodic signals (continuous-time domain signals) with period 2pi/wo have a spectrum with equidistance Delta-impulses of distance w0. 

My question is that, if we have a spectrum with equidistance Delta-impulses of distance w0, does it necessarily means that the time domain signal is periodic? Or for example, if our time domain signal itself is not periodic, like a sin(wt) when w is not a rational ratio, will the spectrum be periodic?!

Also, does a one-sided spectrum with equidistance Delta-impulses of distance w0 correspond to a periodic signal in time domain?
Equidistant Dirac impulses in the spectrum imply a periodic time domain signal.

As pointed out in a comment, in continuous time, the signal $x(t)=\sin(\omega_0t)$ is always periodic, regardless of the value of $\omega_0$.

Your question about the spectrum being periodic is unclear to me.

A one-sided spectrum with equidistant Dirac impulses also implies a periodic time-domain signal, but that signal is necessarily complex-valued because its spectrum has no Hermitian symmetry, as required for real-valued signals.