Am I understanding the phase angle from FFT correctly? Long story short, I have a sinusoidal wave with DC offset going in with a given frequency of say 100 Hz and $\phi = 0$ (which I'm guessing is really $\pi/2$ since it is a sine wave not cosine). I get an output of the same frequency and, using FFT, I would like to find the phase between these two. What I did is I found the peak frequencies (-100 and 100 Hz), found their bin and from the same bin I extracted the amplitude and the phase.

Is that correct?
If you're interested in the time delay between the two signals, it's probably most useful to compute the cross-correlation function of the two signals and find its maximum. The location of the maximum will give you the time lag.