Check which ports are open to the outside world. Helps make sure that your firewall rules are working as intended.
One of a set of tools we are providing to everyone as a way of saying thank you for being a part of the community.
Send on Behalf of: It is what you want to do. To send an email and it will arrives everywhere specifying that it was sent by the account that you used, but... specifying that it was on behalf of another one.
Send As: In this way you can send one email and it will be exactly like if it was other account.
Maybe in your case both permissions are set. If this is the case go to the mailbox that you want to send the message on behalf of. Then open the 'Send As' permissions (you can click the 'Send As' link on the action pane when you select the mailbox) and remove the account from there (as far as it is not what you want).
Later open the user properties and ensure that the permission of sending on behalf is there (As far as you specified, it looks like that this last step you already configured it)