I only have a partial answer using styles, which seems to be what you want to do.
Heading style can be changed to force page break, by going to the modify style box --> paragraph and then selecting tab for "Line and Page Breaks. There you'll find a box for "Page break before," which you should check.
You also want to foce a margin of 7.3 cm. I'm assuming that your document has a different top margin when header is not first line, or else you wouldn't be asking the question.
As you've discovered, however, the "spacing before" attribute of paragraph styles doesn't do anything when paragraph is at top of the page.
The only way I've found to force some additional spacing at the top of the page is to go to the "Border" section of "modify style" dialog. Choose custom border, select 6 pt, make the color of the border white (and therefore invisible) and apply it to top of paragraph only byt clicking above the image of the paragraph. This gets you an additional margin of 6 points.
Then click on "options," where you'll have the option to add space between the top border and text. Unfortunately, this parameter seems to be limited to 31 points. So the biggest increase in points you can get (taking width of invisible border and this spacing into account is 37 points, or 1.3cm. If the "normal" margin on your document was 1.5 cm, you almost, but not quite, have what you are looking for.