Change multiple heading levels

From the navigation pane, drag the section to the correct place (eg, drag dogs between mammals and reptiles) and then you can select 'demote' on the dogs section. This will demote dogs and all its subsections.

The following article shows how to create a list style. I'm going to suppose you already did that, because i'd just plagiarize the article.

http://shaunakelly.com/word/numbering/numbering20072010.html

This will work:

• select all the paragraphs you want to change (thanks to Control-Selection)
• click the "Increase Indent" button

The paragraph numbers will automatically change. If they don't, then the list style isn't properly set.

Have you looked at the Outline view?

In that view, you can easily drag headings and their corresponding paragraphs around and change the level.