Those are just web server logs, you’ll need to find out what your application is actually doing. If not via debug logs then perhaps an strace of the PHP process as it runs.
Sadly that isn’t anything useful.
Afraid not. We know our SMTP servers are up and running, so third party tests to determine if it is or isn’t won’t be much help. You’re going to have to dig into the debug logs for your interpreter (which appears to be PHP). You may need to reach out to your developer or system administrator at this stage, as it seems that you may not be aware of how to configure and work with PHP logging.