ASTRI-Horn is the first Cherenkov telescope with a dual-mirror (Schwarzschild-Couder) optical configuration. It was developed by the ASTRI team as a prototype for the Cherenkov Telescope Array (CTA) and the ASTRI Mini-Array, a nine-telescope array currently under construction in Tenerife. ASTRI-Horn, after its validation with the detection of the Crab Nebula (2020), is currently in a new scientific campaign, also serving as a testbed for novel calibration procedures and technical improvements. Promising results have recently been obtained using the so-called \textit{variance} channel (VAR), a statistical method implemented in front-end electronics, based on the Poissonian nature of pixel signal fluctuations. The VAR constitutes an ancillary output of the Cherenkov camera that provides images of the sky, thus offering a unique opportunity to use stars in the field of view for calibration purposes. By analyzing VAR data taken in the winter of 2022-2023, we measured for the first time the alignment of the Cherenkov camera with respect to the telescope's optical axis with an accuracy of ~1 arcsec, demonstrating the effectiveness of this technique. Furthermore, an optimized version of our custom astrometry software for the Cherenkov cameras allowed us to monitor the position of the source of interest even during wobble mode observations. Finally, VAR data can also be used to assess the PSF of the telescope, allowing us to continuously monitor the quality of optics (alignment and deterioration of mirrors) during scientific observations. These techniques, which are fundamental to the accuracy of ASTRI Mini-Array, can also be applied to CTA.