Is there some type of email framework already built in?
Yes. There are multiple options for most distros. You can use MTA's such as Postfix and Sendmail on most of the larger distros such as Debian, Ubuntu, Fedora, CentOS, etc. It really comes down to what your preference is.
Do I need a MTA or a MUA?
Depends. Most of the Linux distros do come with an MTA and it's typically so that system generated emails can be delivered from various crons and daemons that are running on the system. In these cases the MTA is usually configured to only deliver the email locally to root or an admin type of account on the system.
As far as MUAs, there are a huge variety of choices for these. They range from terminal based apps such as mail and mutt up to Evolution and Thunderbird.
How would I configure the server to be able to send via another host?
I’m not concerned with mail between local users on the box
(There are only 2 so far, my account and root.), but I’m curious how that
works as well.
If you're using a MTA such as Sendmail you can typically configure the box to be a smart forwarding host so that it just blindly forwards any mail that it can't deliver locally to root or an admin account on to some designated host that will take care of delivering mail originating from the host.
How does the “mail” command fit into this?
This is just a MUA.
How does /home/user/maildir fit into the picture?
Only the accounts that are local to the host and that have received mail will typically have email dropped into this directory. The mail showing up here is usually being delivered by the locally configured MTA.
Is this something inherited from Unix?
Not sure how to address this question.
If you're asking about the apparent difference between say a PC that typically doesn't include MTA/MUA types of applications on the box and a Unix box that typically does.
Then I would say the following:
It's more to do with the types of applications that Unix boxes would fill vs. those of a PC. It was generally the norm that most Unix boxes were used as servers, and servers need to deliver mail from a variety of daemons and services that run on them. These services typically didn't have a user account associated with them, so a MTA was required to get system emails out of the box to the rest of the world.
But IMO, I find it unusual that a PC doesn't include these types of functionality, but that's just me 8-).