There's no option to make the width of the navbar smaller. Maybe you mean the height?
In that case, you need to reduce your Logo Width and Navbar Top Height.
Also, remove this code:
Increase the Navbar Top Logo Alignment and the Navbar Top Link Alignment instead of using that.
Button in the Navbar would need custom CSS. @Prasant showed you that you need to add a class to the menu. Here's a detailed guide for that. Once you've added that class, you need to target and style that like a button. That is outside the scope of our support. To make the button/menu a "click to call" link, follow this tutorial.
As you can see here, the issues you're facing are mainly caused and/or could only be solved by custom CSS. We could not continually provide you with custom code as that would be veering into custom development. We provide code to guide you and help you get started. Developing your site especially using custom codes is not a part of our support service. Please see our Terms.
I'd recommend you use Pro as you have lots of header customizations. Adding a button to the header would also be easy.
I hope you understand.