Transparency

Why are you not selecting that black box shape in Pages and copying it to the clipboard, then from Preview, choosing New from clipboard? It is opened in Preview as a png, which you can then copy and paste right back into the Pages layout document, as just the image.

In Layout mode, you can set the Pages background color to transparent, but unfortunately, the exporting, or saving to PDF process forces a white background on the PDF - without override.

It doesn't seem to be possible with Pages. Even a "blank" document has a header strip already inserted at the top of the page.

Doesn't matter if I open that exported PDF in Preview or Photoshop, it opens with a solid white background.

I opened the test PDF in Acrobat Pro, thinking Preview must have added a background to the PDF (by default in virtually any app that writes a PDF, there is no background, even though it displays as white). Surprisingly, Acrobat says there is no background to remove.

Next test was to create a simple document in MS Word. Blank document with a box and saved it as a PDF. That opened correctly in Photoshop with a transparent background. Doing a Save As to a PNG also correctly saved with a transparent background.

Okay, since the PDF from Word works correctly from Photoshop, let's try Preview. Opened the PDF in that and saved a PNG. Preview failed miserably and created a PNG with solid white background.

This proves, once again, that Preview and Pages are free for a reason. They're lousy apps.