We present narrow- and medium-band HST imaging, with additional supporting ground-based data, for 8 galaxies identified as hosting fading AGN. These have AGN-ionized gas projected >10 kpc from the nucleus, and significant shortfall of ionizing radiation between the distant gas and the AGN, indicating fading AGN on ~50,000-year timescales. Every system shows evidence of ongoing or past interactions; a similar sample of obscured AGN with extended ionized clouds shares this incidence of disturbances. Several systems show multiple dust lanes in different orientations, broadly fit by differentially precessing disks of accreted material ~1.5 Gyr after initial arrival. The gas has lower metallicity than the nuclei; three systems have abundances uniformly well below solar, consistent with an origin in tidally disrupted low-luminosity galaxies, while some systems have more nearly solar abundances (accompanied by such signatures as multiple Doppler components), which may suggest redistribution of gas by outflows within the host galaxies themselves. These aspects are consistent with a tidal origin for the extended gas in most systems, although the ionized gas and stellar tidal features do not always match closely. In contrast to clouds near radio-loud AGN, these are dominated by rotation, in some cases in warped disks. Outflows are important only in localized regions near some of the AGN. In UGC 7342 and UGC 11185, luminous star clusters are seen within projected ionization cones, potentially triggered by outflows. As in the discovery example Hannys Voorwerp/IC 2497, some clouds lack a strong correlation between H-alpha surface brightness and ionization parameter, indicating unresolved fine structure. Together with thin coherent filaments spanning several kpc, persistence of these structures over their orbital lifetimes may require a role for magnetic confinement. (Abridged)