So what exactly is this “not secure” message you’re getting? Any specifics or error codes?
I’m guessing the certificate isn’t “self signed” (certificates don’t suddenly become signed in a different way), but rather “not trusted”. Please remember that “self signed” means it’s “not trusted”, but “not trusted” doesn’t mean it’s “self signed”.
This could be caused by the lack of CA chain support on free hosting, meaning any SSL certificate is installed is technically incomplete. For 99% of all browsers, this is not an issue, but it appears that for some of the browsers you’re using, it is.
I don’t understand what you mean. What does WP Super Cache have to do with any of the issues in this topic?