Now I tried both Inkscape and Foxit. No layers. Note also that the screenshot in post #5 shows only a layer 1, but no layer 2.
I don’t know about foxit, but in inkscape you open it and
1) when the dialog appears you uncheck the bottom two checkboxes that converts the fonts and embeds the images.
2) right click on the image and select “ungroup”
3) Click on the image and you should see little arrows show up around the image. Now you can move the individual layers.
I didn’t figure it out the first time either. I had to do it a second time before I figured it out. Good luck.
A lot of novices place multiple objects on the same layer instead of creating new layers.
I’m not familiar with Inkscape or Foxit. I’m using Illustrator CS and Adobe Acrobat Pro.