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How to copy something from a right-hand page and paste it to the exact same place on a left-hand page?
Paste in Place, Ctrl-Alt-Shift-V, will paste in the same location relative to page edges, but I don't know if there's any command that will adjust for offset margins, if that's what you're seeking. I'm sure it could be scripted.
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InDesign works differently - it creates spreads of a book - Illustrator works with Artboards.
Anchored objects are a fantastic way of controlling position of objects as they change page.
They are essentially part of the text - as it's anchored with the paragraphs - so you delete the paragraph you could unintentionally delete the image just a caveat.
I talked a bit here how to do it
I had more comprehensive posts in the past but I cannot find them.