1) That is correct. You need to ensure that you add any domain names as authoritative so that the mail server will accept the mail.
2) You should really create a seperate Receive connector and create as an 'Internet' type connector where Anonymous users are able to send mail to it. You can create another Send connector that will be used to send all outbound mail if you wish, or amend the properties of the existing one if reqd.
3) You need to port forward 25 for mail. You will need 443 if you want OWA availability for users outside.
Shaun