You can resize the image in the tool or set the Pixelsize horizontal/vertical whatever you want, but when you export you do at 1:1 scale. This means that if you impor a 512x512 image and you set pixel size Horizontal/vertical to 4, the exported image will be 128x128, due 512/4 = 128.
About the zoom in/out , yeah the image moves, so be carefull, btw you can double-click on the image to set in center again (if i remember well)
Detail changes in zoom in/out may be for different reasons, like dithering and how other shader works that are not resolution independent, which means you can get some different details in some cases.