Windows 10/Windows 7 should make no difference.

As far as Word 2016/2010 goes, it depends.
Generally, no problem.

If any features that are not in Word 2010 are used, they will not work in Word 2010. Generally it just becomes text. If saved in Word 2010 format, those features will disappear and not be present when the document is reopened in Word 2016.

Word 2010 and 2016 use a different "document layout engine." Formatting may be a bit different. The narrower your margins, the more likely the problem, IMO.