There is a lot of ground to cover that can not be answered easily, but here is my response as a network admin who has setup many AD based networks from the ground up. I will first answer some of the questions.
First, no Exchange does not come with Windows 2003 server. It is a seperate piece of software that requires its own media, license, and install. The goal of exchange is to provide an E-Mail solution mostly used for large scale networks.
If you wanted an exchange based E-Mail env then yes you would have to install exchange on your server box. This would be easy for you because it would be a new Exchange env and there is no migration to perform. During the exchange setup is when you tie things into active directory itself (forest/domain).
When you create accounts in AD you will now see the option to create an exchange E-Mail account in addition to the AD account. This creates a mailbox on the designated mail store.
When the user logs on to the domain it is simply talking to the exchange mail store in terms of mail not authentication. I mean there is way way way more to it, but that is the simplest answer relating to mail only. The POP3 was just an example of another mail type it does not relate to exchange directly. SMTP is just the protocol mail uses.
Again these are very basic answers..if you want me to get more technical please let me know and I can advise.