For me, DSR simply renders the individual frames in 4k, then downgrades to a 1080p frame. Makes for higher gpu usage and a much clearer detailed picture. Biggest downside is it also renders any and all print, including menus, to the point where words are too small to be legible. Sucks in skyrim where I'm constantly in and out of inventory etc and any subtitles or chat is impossible to read. Definitely not blurry at all, but still unusable. Changed to a 1440p render and all great.
The reason you aren't seeing resolutions higher than 1080p anymore is because of the setting that automatically adjusts for viable resolutions according to the monitor. Since your monitor is only capable of a max supported resolution of 1080p, that's as high as its going to show. You can turn that off and you'll see other resolutions, but I'd advise against trying to force the gpu to a higher resolution that's not supported. Good chance of killing the monitor that way.