wouldn't recommend trying to run a mail server for outbound mail on a home connection, inbound sure, outbound no
yes that's normally the opposite way around to what you'd think, but in reality a mail server for receiving you'd have no problems, however for sending email you will find a very large number of email providers/ISPs/etc will block you from delivering mail to them.
due to the large number of users computers that get infected with malware that is then used to send spam most companies block mail from dynamic IP Addresses, they go by the theory that you should be relaying through your ISPs mail server not sending directly, and therefore most of the stuff they get from dynamic IP Addresses is just spam so block it