How can a variable in a header be set to display the first header on a page, even if the paragraph format is different, such as a Header 1, Header 2, etc.?

You can include more than one paragraph tag in the [paratag] part of a building block. When you include multiple paragraph tags, FrameMaker uses the first paragraph it finds with one of the tags. Separate the tags with commas, as in the following example: <$paratext[Head1,Head2]>

… says my old 7.0 User Guide. As far as I remember, there have been other threads about how to interpret first paragraph it finds :-}