Exporting your Pages document to a Word file requires translating the file from Pages's internal format to .doc or .docx format.
Any Pages features not supported in Word (or implemented in a different manner in Word) will likely not survive the translation.
Opening your editors .docx file as a Pages document requires translating the file from .doc or .docx format to Pages format
Any Word features not supported in Pages (or implemented in a different manner in Pages) will likely not survive the translation.
If you are regularly sharing documents with someone using MS Word, Pages may not be the right choice of software for the job.
You may get better results opening your editor's return document using one of the openoffice.org based 'office' applications, such as LibreOffice. The application is free to download and use, but does have a learning curve.
You will get the most accurate transfer using MS Word at both ends of the pipe.
Regards,
Barry