The compatibility check usually fails to detect appropriate apache modules for shared hosting environments. You may need to check with your host to confirm what modules are available, but the mime, rewrite, and setenvif modules are required by wordpress to work properly anyway.
In the text you quoted above "disabled" is as in you can't even check the checkbox, not just that the box isn't checked. You will probably have some options that aren't compatible with your hosting that are still available to be checked, though.
To enable CDN, you first need to set which cdn you want to use on the general tab, save that, then configure the CDN settings on the CDN tab.
I don't think there's any hosting configuration that would prevent you from being able to use a CDN, since most of the work is done on the CDN side, and the only thing that changes on your site is urls get pointed to the CDN distribution for files you're serving from your CDN, which doesn't require any special modules.