Postfix + Courier IMAP local email problems

[Ron]

I'm having a couple of issues with postfix and courier-imap on my new 
machine and I'm trying to figure out what is different from my old 
machine.  I've checked every config file I think of and they both seem 
to be set up the same.

Here are the two issues:

If I send email from a local user (while SSH'd in using the command 
line mail) to another local user (mail todd at mysite.com) on the same 
machine, but using the full email address, I get the following error and 
the email bounced back:

553 5.3.5 mail.mysite.com. config error: mail loops back to me (MX 
problem?)
554 5.3.5 Local configuration error

The only thing I can think of is that mysite.com and mail.mysite.com 
(the mx record) do not point to the same server (which they did on my 
old machine).  I have also tried everything I can think of in how users 
are listed in postfix's virtual file and in /etc/aliases and server 
entries in main.cf.

The second issue is if (again, SSH'd in an using mail) I send email to 
a local user without the @mysite.com (mail todd) then the email isn't 
available via IMAP externally.  I can read it using the command line 
mail, but not externally via IMAP.  These two mailboxs are completely 
separate and have two different lists of waiting email.

Everything works fine if I send email from a remote client 
(Thunderbird, Mail.app) and read the email with a remote client via 
IMAP.  It's just the local email sending that seems to be broken.  I'd 
like to get one of these two problems fixed so root can email me daily 
log files, which it can't do right now or I can't read via IMAP because 
they are't going to the right mailbox.

Is there some simple I'm just messing up?