Why are page headers and footers not shown in Office web apps?
The documents that you open in the web applications for Word, PowerPoint and Excel are the same as the documents you open in their desktop applications, but some features work differently in the two environments. The web applications let you make basic editing and formatting changes. For more advanced features you need to open the documents in their desktop applications, using the Open function in MetaShare, or by selecting the "Open in Desktop App" command, in the web application:
Note that you will not get the "Open in Desktop App" option, in the web application, if you are opening a document that is shared to you from another Office 365 tenant.
One of the more annoying thing with Word's web application is that it, by default, does not display the documents' page header and page footer. You can however see these elements by clicking on the "View" menu and there select the "Reading View" option, to see the document with all elements, the way it will look like when you print it out or by selecting the "Header and Footer" option, to edit the header/footer:
Here you find some more extensive information about the differences in the apps: