Hi, Benjamin,
In the header of your first page, click the box for "Different first page." After you click the box, insert your header.
Now go to the last page of your document. Insert a section break at the top of the document (not in the header area but above any text you have in the body of the document). Do that by going to Insert > Break > Section break (continuous).
Put your cursor in the footer area. Click on Options. Under "Apply to," select "This section (Section 1)".
Press the blue Apply button. Enter the content you want in your footer. It should now only show up on the last page (as long as you don't add more pages after that).
~Jo