What do you mean by "and I do"? If you drag an image onto the model window, it will prompt you to do that yes. So, I assume you either want to make a decal or a rotoscope....right? Pick which one and click OK.
Images are never embedded. Ever. The project file would increase hugely. Models can be embedded and are when you chose "Embed ALL" or individually in the file properties.
In your middle image, you know what file isn't embedded because it has a floppy disk in the icon in the PWS.
As for the white lines....your main body is duplicated...To fix it, select a point on the body. Press the / key. Now move the duplicate out. There's also some patches that need to be flipped on it.