Hi Jose,
The logo and search icon can not be clicking issue is caused by content added via a plugin, as you can see in the below screenshot, the blue part is the invisible content, it’s on top of the logo area, so the logo and search icon can not be clicked after the initial load:
https://www.screencast.com/t/TGVm3LytIf
I’m not sure what plugin it is, would recommend disabling all plugins except GP Premium to test.
As for the search modal position issue, the GP theme you are using currently is still a developing version, I’ll report the issue and try to fix it in the official version 🙂