One more thing. you said...unless you specifically attempt to access a computer at a remote location. Would an extreme end of my house count as a remote location?
No, by "remote" I mean external to your local network. Any devices on your local network would be behind an Internet router. Any traffic destined for the local network, again, passes through this router but only on the local side of the network.
In one room I have a mac with my music on it. I tried with blue tooth to see if I could connect and I couldn't.
Yes, bluetooth has limited range. I would not expect that you would be able to access anything in another room using bluetooth.
But with the airport plugged into the modem, I can view my music on that computer from my laptop on the other end of the house.
That's because if you're using screen sharing that is happening over a network, either wired or wireless, between the two devices.