Re: current noise
My first point is that semiconductor junctions are only one possible case of current sources that involve charge carriers transitioning a barier, so that independent events are generating a possion statistics. Photoelectrons are another case and I guess, also charge carriers tunneling an isolator. The latter is probably a model for MOS gate current.
But you should ask a semiconductor specialists, I'm only a hobbyist in this regard. If the discussion is about CMOS IC, most of the input current is from surrounding junctions rather than from gate oxyd. So no matter if gate oyxyd current has shot noise, the junction current surely has. JFET gate current anyway.
Finally, if you look at a CMOS OP datasheet, you'll notice that the low frequency noise current density (that may be thought as caused by shot noise) is constant up to a few kHz only, increasing considerably with frequency. Obvioulsy other noise sources are dominant here.