Hi,
1. Are you using any 3rd party plugin to alter the view/contents on that page? That may cause the conflict here.
2. I might be missunderstanding here something. I checked the search page, but the theme text seems to be okay at the moment. This sounds like an issue with the minification/cache, as I see there is something minifying and combining the CSS files. Is there an easy way I can replicate this issue?
4. Well, try in this case try looking for the searchform.php file in the theme directory, that usually holds the default search bar – however if that file exists, then it should be replaced automatically. If you find that file, then try to clear your site cache to make sure it is not an issue with that.
7. That should clear on the mobile devices as well, make sure to clear the device cache, that will do the trick. I just tried via one of our mobile devices, and it worked like that.