The summit of the Antarctic plateau, Dome A, is proving to be an excellent site for optical, near-infrared, and terahertz astronomical observations. Gattini is a wide-field camera installed on the PLATO instrument module as part of the Chinese-led traverse to Dome A in 2009 January. We present here the measurements of sky brightness with the Gattini ultra-large field of view (90 degrees X 90 degrees) in the photometric B-, V-, and R-bands; cloud cover statistics measured during the 2009 winter season; and an estimate of the sky transparency. A cumulative probability distribution indicates that the darkest 10% of the nights at Dome A have sky brightness of S-B = 22.98, S-V = 21.86, and S-R = 21.68 mag arcsec(-2). These values were obtained during the year 2009 with minimum aurora, and they are comparable to the faintest sky brightness at Maunakea and the best sites of northern Chile. Since every filter includes strong auroral lines that effectively contaminate the sky brightness measurements, for instruments working around the auroral lines, either with custom filters or with high spectral resolution instruments, these values could be easily obtained on a more routine basis. In addition, we present example light curves for bright targets to emphasize the unprecedented observational window function available from this ground-based site. These light curves will be published in a future paper.