To define a transparent background for the Primary Navigation, please go to the WordPress  Dashboard > Divi > Theme Customizer > Header & Navigation >  Primary Menu Bar, open the Background Color option and set the opacity level:

You can modify the menu height in the same settings. Look at the first option called Menu Height:

Now, if you need a solid background color when you scroll the page down, you need to check exactly the same option but under the Dashboard > Divi > Theme Customizer > Header & Navigation >  Fixed Navigation Settings. 

Also, if you want the Fixed Header to be exactly the same size as the Primary Menu, define the same Menu Height value for both navigations.

Here is an example of how it will work:

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