Nelson,
In response to #1, there is nothing I can do, support may have to manually change this one for you. I had a similar problem, but they removed it, and it worked fine when I added it again. I think there is a bug in the CPanel software however (its a third party application that lunarpages uses). Last time I heard, there was rumours of a custom lunarpages control panel program that will get around the issues some people have been having, but its not been officially released yet!
support@lunarpages.com is your best bet for this one.
Does it show up as: subdomain.yourdomain.com or as a seperate domain?
2) When did you signup/transfer your DNS? I found that when I transferred my DNS, I had some strange problems similar to that, and when the domain finally pointed correctly, and not just on my computer the issues went away. Give yourself 24-72hrs before you get too worried.
As a temporary fix, you can always use your main domain to send email through until the otherone moves over properly.
Are you using the correct method of logging in to it? Just something to try, try authenticating using your main username and password (the one you use to access CPanel). Basically, since they are both at the same server, you should be able to authenticate with this no problem. If that doesn't work, then it is most likely a DNS/domain transfer issue that should go away. If that does work, then double check that you have your username setup correctly. Make sure you are selecting the authenticate with SMTP server. The Lunarpages server require that you login to send mail, so that other non customers can't use your server, or domain name to send spam.
Hope you get it working, let us know if any of those suggestions worked!
- Ed
P.S. About those good reviews on lunarpages.. they are true (and no, I dont get anything for saying that!). Other hosting companies advertise good support, and when I emailed them... some of them have not responded yet!

Lunarpages got back to me within about 30mins with a detailed answer.