You can create an image field in Acrobat DC. In the image you can paste screenshot or other PDF files, and Acrobat will even attempt to create a PDF of a word file or powerpoint, where you actually get to choose the slide (though I would not recommend it).
If you want to copy and paste elements you are not really talking about form design, because the nature of a form is a fixt set of content holders that are filled with various content.
You can copy and edit PDFs with Acrobat, but I would really question what you are trying to do. How do you plan to process the data that you collect using a form that has no structure?