The lead halide perovskite nanocrystals embedded into a glass matrix exhibit strong interaction with light and demonstrate exceptional optical and spin related features along with long-term chemical and physical stability. We apply the optical spin noise spectroscopy technique to study the spin system of CsPbI3 nanocrystals in the depth of the glass matrix. A pronounced spin precession peak with an isotropic g-factor absolute value of 2.7 and record dephasing time of T2,e = 2.7 ns is ascribed to resident electrons in the perovskite nanocrystals. The experimentally observed Faraday rotation noise with no noise of ellipticity is explained by saturation of the inhomogeneously broadened optical transition. Increasing the probe intensity, we went beyond the non-perturbative regime and observed a number of light-induced effects. The illumination with shorter wavelength light gives rise to a persistent recharging of the nanocrystals by holes (|gh|=0.17 and T2,h∗ = 1.4 ns, T1,h ≥ 30 ns), which remains stable over multiple cycles of heating to the room temperature and cooling. In addition, elliptically polarized light induced an “optical” magnetic field on the system due to the AC Stark effect, which was proven by a new modification of polarization noise spectroscopy.