Hi,
I’m not exactly sure I get what you mean.
Can you explain a bit more?
For the top of the header, perhaps you meant Top bar?
https://docs.generatepress.com/article/top-bar-widget-area/
If so, you should be able to insert a navigation menu on the Top Bar using its respective widget.
Can I use some internal CSS on the home page in the header?
Did you mean, you’re trying to add the CSS something in the content rather than in the <head>
?
If so, you can add <style>...</style>
within a Hook Element and hook it anywhere you prefer.
https://docs.generatepress.com/article/hooks-element-overview/