Hi i have two questions:
Its about this site. www.vonirgendwo.de
How do I remove the white background in the Header ( The Color behind the Logo and Social Icons) ?
How can I add the searchbar under the social icons? (I already found a thread about this but it didnt worked for me, maybe as a beginner i need a little bit more detailed information)
And another question:
How can I move the menu-bar to the left, so that it starts with the blogborder?
When I try it with margin only the font moves or only the bar and everything starts to look like an chaos.
Okay, I got the last question about the menu bar. Just changed float:none and margin-left: -20px …now this works. So just need help with the first two questions.
Okay…I’m so sorry for making this thread to fast. But I now also found the way to remove the background…now only the problem with the seachbar is left! 
There are plenty of options how to add search bar in the header. About one that I can recommend you can read here.
You can also add it directly inside header-extensions.php in similar manner like I described to add custom info there.
Basic search form can be called by using this WordPress function
<?php get_search_form(); ?>
You can read more about it on official WordPress documentation.