Has Apple done anything about the behemoth that is iTunes?
No--at least, not yet. The version of iTunes on the beta of Mountain Lion we have is 10.5.3, the same one that's currently shipping. This may change before Mountain Lion launches, but we don't know for sure.
What cool features are in store for Mail in Mountain Lion?
Mail has three new features: VIPs, inline find, and selective notifications. VIPs are special contacts, chosen by you, whose messages are treated differently from other contacts. For example, you can set Mail to use Notification Center to alert you only when Mail from VIPs arrives. You can also use Mail Rules to filter items from VIPs in a different way. Inline find works much like it does in Safari or TextEdit--hit Command-F, and you'll be able to search the body text of a message. Selective notifications allow you to choose what messages show up in Notification Center--useful if you don't want to have your screen flash every time you get a spam message.
So iChat is becoming Messages. Does that mean I'll be able to send messages to people with an iPhone, iPod touch, or iPad from my Mac? How will that work?
Yes, you can use Messages to chat with people between Macs and iOS devices--iMessages are Internet-based, and thus can be sent between two devices running the Messages app. If you have contacts you iMessage but don't IM, you'll need to type in their phone numbers or email addresses manually, or add them to a buddy list anyway--just as you would in iChat. If you use Messages to send iMessages and your iPhone and/or iPad are nearby, you'll receive your replies on all your devices, along with your Mac.
Can I still screen share, host video conferences, and use iChat Theater?
You can, though that functionality requires an AIM account, rather than an iMessage one. Video chatting can be done on AIM traditionally, or you can launch the FaceTime app through an embedded button in the chat window.
What happens to FaceTime?
FaceTime is still there. FaceTime sessions take place within the FaceTime app on the Mac. Though Messages offers integration with FaceTime--you can kick off a FaceTime session from within the Messages window--it doesn't actually do the FaceTime part itself. That's still a separate app. (Other video chats and screen sharing still occur within Messages, as they did before when it was called iChat.)
Does Messages for Mac have a background listener for messages? Or must I have it open in order to receive messages?