I already have a document with numbered headings. However there's no period after each heading numbering. How do I add that?
Use the Multilevel List Editor to create all numbered lists and headings. Using the Numbered List dialog usually ends up in grief, as does the use of the Paragraph editor.
I refer you to Shauna Kelly's website, Making the Most of Word for your Business.
Look at Step #1 and go from there to the instructions to create numbered headings that won't blow up in your face ;-)
Using multilevel lists allows you to set the numbering type (1, A, I, etc.), add other text to the headings (e.g., Chapter, Section, etc.), set the fonts, set the indents, and add tabs.
(Trust me, when Word's barfs on your headings, it is not quick fix)
Shauna died many years ago, but her site is kept alive to benefit Word users.