1 - I assume that you apply the "jitter" by altering the values of succesive samples. Theoretically, this may generate components outside the Nyquist bandwidth. Do you filter the results before writing the output file? "Real jitter" also generates components outside the Nyquist bandwidth.
The signal is oversampled for the jitter simulation (which is a variable delay modulated by a mix of filtered noise and several sine waves), to minimize aliasing and interpolation artifacts. Components are indeed produced above the original Nyquist frequency (e.g. 22050 Hz), but the downsampling process filters them out.