You need to copy:
/vendor/magento/module-checkout/view/frontend/page_layout/checkout.xml
in your theme:
/app/design/frontend/**YourVendor**/**YourTheme**/Magento_Checkout/page_layout/checkout.xml
Checkout.xml need looks like:
<?xml version="1.0"?>
<layout xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_layout.xsd">
<referenceContainer name="page.wrapper">
<container name="header.container" as="header_container" label="Page Header Container" htmlTag="header" htmlClass="page-header" before="main.content"/>
<container name="page.top" as="page_top" label="After Page Header" after="-" />
</referenceContainer>
</layout>
And then just move logo in your checkout_index_index.xml
/app/design/frontend/**YourVendor**/**YourTheme**/Magento_Checkout/layout/checkout_index_index.xml
Content of checkout_index_index.xml:
<?xml version="1.0"?>
<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" layout="1column" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
<body>
<move element="logo" destination="header-wrapper"/>
</body>
</page>
Good luck and don't forget Flush Cache ;)
PS. Main Navigation is hidden with CSS by default Luma style. You need override CSS to.