You left out some very important information. First and foremost, what domain name do you want to use for email? The fact that your adsl connection is listed as myconnection.myisp.com has no relation to your domain name. Your ISP can call you myconnection.myisp.com, and you can call yourself mydomain.com or workdomain.com, and there is no problem with that.
Again just because you are called myconnection.myisp.com doesn't mean you can necessarily send/receive mail with that name. That would be handled by the server that runs mail (look at the MX record through DNS) for myisp.com.
What you probaly want to do (though I can't be certain) is to register or at least use your own domain, and configure this server to be the mail host for that domain. If you register a domain (mydomain.com), then I would call this server mail.mydomain.com, and point the DNS to the IP address of your ADSL connection. Since you stated the server has a local addresss on your LAN, you'll need to use the router/firewall to forward all traffic for port 25 (SMTP) on the WAN IP address through to your internal. If you want people to access the email from outside the office, you'll need to forward 110 for POP3 access, and/or 143 for IMAP.
Mail sent by smarthost no local mail is not at all what you want for a mail server. I feel that if you want to have a functional mail server, the easiest newbie mail server setup instructions can be found at http://qmailrocks.org
If you want to stick with exim that is ok, but I suggest getting a better understanding of how email/dns works before trying to configure a server. You can google for those explainations.