The plugin will work with those warnings without problems. There is a fallback method implemented if those directories are not accessible.
Putting FTP details into the wp-config.php file shouldn't be a security concern, because the database access is also stored there as plain text – it's a commonly used method with wordpress.
The inaccessible front-end is not caused by the permission issues, I'm 99% sure. The screenshot didn't get through for some reason, can you please re-attach it?
If there are any error messages that you can copy/paste here, that would help a lot as well.
I believe we can still make it work despite the restrictions. If I can see any notifications, error messages, that I will be able to tell what's the possible cause.Best,
If you like my products, don't forget to rate them on codecanyon :)