In postfix, how could I disable incoming mail?

You can use the inet_interfaces directive in /etc/postfix/main.cf to control what address Postfix listens on for incoming connections. If you set it to the following it will only listen on the loopback interface, which means that connections can only originate from that machine.

inet_interfaces = loopback-only

You can disable incoming SMTP by editing master.cf, just comment out the smtp and submission services. This will tell postfix not to spawn an smtpd process, which would listen on port 25 (587 for submission) for incoming SMTP connections.