My header height needs to be reduced and header on all pages of my book is wider than footer.
Headers and footers can be formatted:
menu Format | page style | Header - Footer
If your entire document is based on only one page style the alteration of the specific page style affects every page (which is based on the specific page style).
Get more information from the manual (you may download as PDF file):
https://wiki.documentfoundation.org/Documentation/Publications
English documentation | LibreOffice Documentation - Your documentation for LibreOffice
From the question wording, I assume you are not familiar with styles and that you document has therefore a uniform presentation (all pages are identical).
Format>Page Style will open the dialog for the current page style, likely to be Default Page Style.
Header tab controls header properties, but, by default, headers are AutoFit height, meaning space is allocated dynamically according to header content. Reminder: header estate is taken from the “active” area from the page, i.e. the space left when you remove margins.
It may be that the margins (which are an absolutely no-print area in Writer, contrary to Word) are already too large for your purpose. You can adjust them in the Page tab.
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