I have no idea what you mean by setting the background.
That said, for anything other than most simple forms, you're going to need to do some work in Acrobat.
If you have very specific questions about that, you should probably move to the Acrobat forum and ask there.
In Adobe Acrobat DC, instead of opening the pdf in Acrobat, I set the pdf 'as a background'. That way, if I have to make another change in inDesign, I can upload a new pdf 'background' without disturbing the fields/drop-downs/etc I've created.
So the steps are:
Edit/Make the document in InDesign > Export as PDF > Open Acrobat DC > Open new, blank document or Open Pre-existing Document > 'Edit PDF' Toolset > Select 'More' > Background > Add
When working with single-page PDFs this works flawlessly. I have to adjust the fields slightly after, ofcourse, but I don't have to try and recreate the fields or make an entirely new document. The issue is is that when you create a background this way, every page gets the same image as a backdrop so working with multi-page pdfs exported from inDesign is difficult. I guess this was meant more for creating flyers or something or a booklet/pamphlet with the same images over and over.
I think I actually found a plugin that kind of does what I want, but it costs ~$200. It's on this page (item # 4) The 15 best InDesign plugins | InDesign | Creative Bloq
Have you tried the replace pages command in Acrobat. Seems like it would be just what you need.
Haha, that looks like it was exactly what I wanted! The fields don't move but the page changes. Thanks a lot. I was a little distraught.