More accurately, styles break when = Header = is used after {{examples}} template. Which is how they are used on "Type 1 examples: ... Type 2 examples:" pages.
Also, this does not show in preview, only after saving the page.
I made a sample page in my sandbox.
Note: edited your post to fix that link.
As for the busted headers, that's normal. For one, level one headers are the page title in MW, level two are == Title == sections, Level 3 the === Title === sections, and so forth.
What you are seeing is MW's confusion at the improper use of header levels.