Unfortunately, none of these rings appear genuine:
1. The top ring with the elliptical bezel is suggestive of Hellenistic Greek and Roman Period artifacts. Most bezels are slightly concave, although Classical Period examples made of gold are sometimes convex. Imagery is fairly standard. Possibly Pan, Dionysus or some demi-god presenting offerings before a thymiaterion.
2. The second ring with the round bezel is similar. Fairly generic motif of Pan, satyr or other male figure, possibly before an altar. Engraving of woodland and nature deities often include accessories such as trees, branches, floral sprays, etc., as associations to agrarian origins.
3. The bottom pics are of a two piece ring with a rectangular bezel. While the first two offerings simulated oxidative damage (artificial aging), this last is an unpretentious modern piece with standard neo-Classic imagery. Maybe the dealer purchased it at a gift shop, or thought it up himself/herself after studying Wedgewood designs or antique Venetian wallpaper.
Just my two cents ......................... Gaius