Can you clarify what you mean by changes on the header? If you are editing the core files you should do on your child theme and that won´t be overwritten, but I don´t see the need to change the core files to achieve the layout you are looking for.
You need to create two bars in Pro.
The first bar, you will add 3 containers. The first container you will a text element and your calendar shortcode.
The second container you will add the logo and on th third another text element and add your content there.
On the second bar you will add your inline menu element which you will click on the customize tab and hide for the smaller screens and add the mobile menu element, click on the customize tab of the element and hide for the larger screens where you have your inline menu showing.
Hope it helps