If you remove header/footer from a page of a Word doc, header/footer from the entire document disappears. Similarly, if you insert header/footer to a page, the same is copied to entire pages of the document. This is how header/footer supposed to work.

Now, if you need to apply unique header & footer to a page or part of a document other than the rest of the document, how will you do that?

The trick lies in separating the pages which would have unique header/footer from the rest of the document using Section Breaks. The separated sections can be applied with unique formatting and styling.

For example, suppose the pages 5 to 7 in your document to have a unique header/footer than the rest of the document.

The Procedure

1. Insert Section Breaks at the end of the pages 4 and 7. This way, you have divided the document into three sections. To insert a Section Break, do the following:
2. From the Word Ribbon, click the tab Page Layout and then click Breaks under the group Page Setup. From the drop-down list, click Next Page under Section Break. See below screen.

1. Now on the 5^th page, enable the header/footer sections by double clicking the top/bottom of the page respectively. The Header & Footer Tools tab is enabled on the Word Ribbon.
2. From the Header & Footer Tools tab, under the group Navigation, click the Link to Previous icon  to de-link the current section from the previous section. This is the key step of the procedure.
3. Now, enter new header/footer content on the 5^th page.
4. Similarly, enable the header/footer section on the 7^th page and click the Link to Previous icon to disable the linking between current and previous sections. On this header/footer, you can repeat the header/footer of the first section.

Please go through the following article to understand how to remove header and from the first page:

https://wordknowhow.wordpress.com/2013/04/04/how-to-remove-header-and-footer-from-the-first-page-of-your-word-document/