How to get the MX record (what you need) is actually already covered in the FAQ. HOWEVER, don't do this. This is the job of the mail server, not a JavaMail API-based program. Use your own mail server program like James to send mail if you can't figure out how to get your ISPs to work. Of course, figuring out the issues with your ISP is the easiest way.

I don't think you can get an answer on this question; all (or at least most) SMTP server are all protected against out-of-domain use. The SMTP server checks the IP number of the user that want to use the service. If the IP number is not listed in his access list you get the message "-ERR We do not relay". This is to block spammers. The easiest way to send an email is to install your own SMTP server. If you check the JavaMail homepage from Sun you see a few SMTP providers listed there. I do believe there is an SMTP server implementation in Java available.