LibreOffice Writer apparently cannot fold/unfold sections à la NotePad++.
I find this easier when working on longer documents.
Does MS Word do this?
Yes. Can be seen in the Document Map - in the example the text is repeated and contracted at the top and then the same below without contraction. Clicking on the + would 'duplicate' the tree (ie expand the top half to be like the bottom already is).
In Word 2007 Levels can be controlled in View > Document Views - Outline but are already built in to some standard styles.
ConstEdit is a word processor that uses the html format for its documents. It has section structure management functions that is close to your requirements but not exactly. You can go to any particular section quickly and move sections around without using cut and paste. It however does not support fold/unfold of section. (Disclaimer : I am the author of the app)