Things to check:
While typically this is in /var/log/maillog, it can vary based on control panel server. Check where mail log entries go by looking at /etc/syslog.conf
2. DNS Resolution on your server.
If you log on as the root user, can you get to outside sites.
Use nslookup or dig to check if you can get the proper mx records for cnn.com (for example).
You can do a dnsreport.com report or use DNSstuff.com to find out what the answers should be set to use.
3. Yes, you can shorten the queuelifetime to 2 days.
4. You may want to consider setting up and using RBL's (real time black hole lists).
for a reasonable comparison of various RBL providers.
5. Also, check for mail loops (checking mail logs will help).