Hi Jurgen,
You can make the header disappear by adding the following CSS code in the Custom CSS option of your theme on the below path.
Admin Area -> Appearance -> Customize -> Travelify Other Options
#branding .hgroup-wrap {
display: none;
}
If you want header to be smaller then instead use the following CSS code.
#branding .hgroup-wrap {
padding: 0;
}
#branding .hgroup-wrap .hgroup-right {
margin: 15px 0;
}
To move social icons in the menu list, please use the solution shared in the following thread.
https://colorlibsupport.com/t/align-social-icons-at-the-top-next-to-menu-names/#post-40360
Best Regards,
Movin