The full range of the data is plotted, it is the origin that is different. Is this what you are looking for?
plots = ListLinePlot[#,
Background -> Black,
ImageSize -> {128, 128},
Frame -> True,
Axes -> False,
AspectRatio -> 1,
PlotRange -> All,
AxesOrigin -> {0, 0},
PlotMarkers -> {{\[FilledCircle], 2}}] & /@ images

Regarding Binarize, it requires an Image or Graphics as input. Framed changes the Head to Framed. So, Binarize first, then add Framed.
plots = ListLinePlot[#,
Background -> Black,
ImageSize -> {128, 128},
Frame -> False,
Axes -> False,
AspectRatio -> 1,
PlotRange -> All,
AxesOrigin -> {0, 0},
PlotMarkers -> {{\[FilledCircle], 2}}] & /@ images
Binarize /* Framed /@ plots
