No, I am not saying that the top Finder window is not there on pristine machines. What I am saying is that it has been altered, and that it appears that certain things were added, and then removed at some point, which would explain those two large question marks.
Also, the toolbar has been customized. Both the "Path" and "Quick Look" buttons were added. You can customize the toolbar by right-clicking in the toolbar area, and then selecting "Customize Toolbar". In Mojave, the default toolbar looks like the image below.
So the question still remains, where did that second "search for:" field come from? You -- or someone else -- must have installed some app or system extra at some point to make that happen.

I am not familiar with an app called "Customize Window" or any Houdah products, but if they are search apps, then yes indeed, they could very well have inserted that second search field there. I would try uninstalling them -- hopefully with an installer from the developer -- and see if that second search field disappears.