Adding Additional menu link on mobile and menu background color

I was trying to create a different mobile menu that adds a Home page link. (Or maybe I can only show this primary menu link on mobile?). I almost got there by using secondary menu for mobile, but can’t style it. I was also able to solve the menu on mobile not closing by adding the full page link but only downside is that link is likely also highlighted if you don’t edit your active link colors on the menu. Any ideas on best way to add an extra home link on mobile on this theme appreciated! Lastly, even though you can choose mobile menu background color, I can only get it to be black or white?