You can fix these two issues with native Cloudflare feateures:
Automatic HTTPS Rewrites
First, enable the Automatic HTTPS Rewrites to prevent the Mixed Content problem.
Always Use HTTPS
Now, enable the Always Use HTTPS to redirect all http:// requests to https://.
In addition to what @domjh pointed out about Mixed Content: While Cloudflare handles this issue perfectly, it is recommended that you rectify your server and/or CMS settings to avoid future issues.