The numbering of headings is 100% done in Word.
You need to make sure that the Heading 1, Heading 2 etc in Word, which eaDocX uses by default, are configured to use the numbering style you want.
This style will need to be in the Word template which eaDocX is using: Normal.dot is the default, so the numbered heading paragraph style needs to be in there.
Quite easy to test – just create some new headings manually in Word, and see if they get a heading number. Then save those settings as a new .dot file, as normal.dot, and eaDocX will pick up those styles and use them.

This also sounds like a Word paragraph style issue.
The section marks are created by eaDocX with a Word style which says ‘invisible’, which means they can be seen only where you switch on ‘shown invisible text’ – which is what the ‘toggle section marks’ command does.
Probably means there is something in Word which is making this ‘invisible’ text visible.