This needs extensive code customization which is indeed outside of our support scope. You will need to read the articles below to get started:
The file which is responsible for the place of the header items is:
You will need to create necessary folders and the file to your Child Theme.
Even if you can change the place of the items you need to add additional CSS stuff to do make it sit as you wish.
The other alternative is to convert the X to Pro which you can use the Header Builder to have the same kind of header:
For more information about the header builder I suggest that you check the video below:
Please consider that Pro does not have the Demo Import functionality of the X and the Cart Icon is different from the X and you need to be aware of that:
If you ever consider for the conversion you can use this article: