Hi,
1. It is a server side issue for sure, the most likely cause is a 3rd party plugin or the theme. The best course of action in this case is to disable all plugins one-by-one to see which may cause the conflict. Maybe cross-check with the staging server to see which plugins are not present there, and turn those off first. If you are using any custom codes related to any plugins, I would disable those as well just to be sure.
Unfortunately the error message does not include any further details, it is supressed. However wordpress should notify you via email if there was an error, with the exact error codes. If you have access to any of the server error logs or you can turn on the error reporting, that will surely tell what exactly is causing it.
2. I assume you are reffering to the search icon on the bottom of the screen – that is not added by our plugin, it is probably a theme feature. You may need to ask them about that.