Your own port 25 being open has nothing to do with outgoing email.
If you're getting connection timeouts to big email providers like Google and Hotmail I would suggest one of three things is happening:
- Your ISP blocks outbound port 25. This is increasingly popular on home ISPs to stop spam. They will force you to use their central mailserver.
- You are inadvertently blocking outbound port 25. This would be something you've actively done. Check your ufw/iptables rules for spurious deny rules.
- The remote services are blocking you.
But double check the real log with sudo less /var/log/mail.log
and make sure you're not missing any obvious issues your pretty logs above aren't showing.
You can also debug more simple network issues with simple tools:
ping mx1.hotmail.com
If ping fails, there's a serious network-level issue. You managed to look it up in the first place so DNS should be fine but if you can't ping it that might suggest you're being blocked completely.
telnet mx1.hotmail.com 25
That should open up a raw connection to the remote mailserver. If that doesn't work, you know it's not postfix that's tripping over.