We present new Hubble Space Telescope Advanced Camera for Surveys imaging of six positions spanning 5.8 kpc of the H I major axis of the Local Group dIrr NGC 6822, including both the putative companion galaxy and the large H I hole. The resulting deep color-magnitude diagrams show that NGC 6822 has formed >50% of its stars in the last ~5 Gyr. The star formation histories of all six positions are similar over the most recent 500 Myr, including low-level star formation throughout this interval and a weak increase in star formation rate during the most recent 50 Myr. Stellar feedback can create the giant H I hole, assuming that the lifetime of the structure is longer than 500 Myr; such long-lived structures have now been observed in multiple systems and may be the norm in galaxies with solid-body rotation. The old stellar populations (red giants and red clump stars) of the putative companion are consistent with those of the extended halo of NGC 6822; this argues against the interpretation of this structure as a bona fide interacting companion galaxy and against its being linked to the formation of the H I hole via an interaction. Since there is no evidence in the stellar population of a companion galaxy, the most likely explanation of the extended H I structure in NGC 6822 is a warped disk inclined to the line of sight.