for the eyes make sure the pupil UV is within the image bounds and set it the extension type (the property that is set to repeat by default on an image texture) to clip, for the body you need a texture coordinate, connect UV to a separate XYZ, and connect X and Y to math nodes with ping pong (second value is 1) and then connect them to the corresponding inputs on a combine XYZ, which you plug into the vector and finally, set the extension type to extend
here are four images to show what are the differences between https://gofile.io/d/cy3ban with and without the mirroring setup, and extend/repeat extension types
here are four images to show what are the differences between https://gofile.io/d/cy3ban with and without the mirroring setup, and extend/repeat extension types