Although the PDF format gives the promise of cross-platform interoperability, there are many different applications that generate PDFs including Adobe LiveCycle Designer on WIndows that take poetic license with the PDF content generation, even to the extent of referencing Adobe Acrobat plug-ins, or Adobe specific Acrobat JavaScript (AcroJS) to control PDF forms. There are also many different PDF readers that vary in their abilities.
The PDF reader that comes the closest to managing the potential PDF variants from the first paragraph is Adobe's own free Acrobat Reader DC. Apple's Preview is based on older PDF technology and there are PDFs that it will not handle well or at all.
There are several PDF editors that can generate a Word document from a PDF, but no one does PDF to Pages well as Apple has not provided the Pages internals documentation to third-parties. Best to go to Word and then open the Word document in Pages.