Hey Robert,
it is possible to add links or text into the header but it depends on the position you want to add them. In general the Shopware Theme is divided into Smarty blocks (https://developers.shopware.com/designers-guide/getting-started/#template-blocks).
So you can just go to the “Bare” theme, head to the “frontend/index/index.tpl” file and look up the position you want to extend. Now you’re creating a new theme (using either the button in the Shopware Backend or using the CLI command - see: https://developers.shopware.com/designers-guide/getting-started/#custom-themes). Create a new file “frontend/index/index.tpl” and extend from the inherit template file:
{extends file="parent:frontend/index/index.tpl"}
Now just place your block into the newly created file and add the content you want. The rest is just styling 
I would recommend looking into our designer’s guide to get used to the inheriance system: https://developers.shopware.com/designers-guide/theme-startup-guide/
Best regards,
Stephan Pohl 