@birken if you were able to reproduce a blank page without code, what you have done is perfect. I’ve posted that code because usually the theme doesn’t give you the possibility to show a page without header and footer, but I suppose in your case you can do it, so you don’t need any code.
The server cache is a problem when, the server sends something different to mobile and desktop devices, as in this case. No matter if you do it with this plugin or in another way.
As you probably know, when a page is served by server cache, that page is not dynamically generated every time the user request it, but a static already generated page is sent to the user browser. The cached page is generated when the user visits for the first time that page, then other users will see the cached version.
So, imagine the following scenario. In the beginning, you have no cache. A first user visits your page with a desktop device, so a blank page is saved in the server cache.
Next user visits the same page with a mobile. On mobile, you don’t want to show a blank page, but because the cached version was generated visiting the page with a desktop, also the second user will see a blank page, also on mobile.
If you want server cache, better you use a plugin that gives you the possibility to distinguish between desktop and mobile, as e.g. W3 Total Cache, or WP Fastest Cache. You have also other plugins that can do it.
You can set up this kind of plugins in a way that the mobile cache is generated only when the user visits the page with a mobile, and the desktop cache is generated only when they visit the page with a desktop. In this case, the cache will not give problems.