For some reason, I have know outgoing messages, in my PM's. I've got a bunch of "inbox" but no replies in the "outbox"?  Is that normal, or is mine messed up?

By default, it is disabled. When writing a PM, click on the "Save a copy in my outbox" check box which is below the box you type in.

You can set this box to be checked by default on all PM's you send. It is in your profile settings.

Click "Profile" in the top menu bar of the site, then in the menu on the right, click "Personal Message Options", then check the box next to "Save a copy of each Personal Message in my outbox by default."

Let me know if you have any other questions.