It means that your Apple TV will only work with that one remote. The Mac which has not been paired, will still accept any remote input. The solution is to pair the Mac with it's own remote or turn off the IR receiver in the Mac in the Security Pref Pane.
I think he is talking about the remote app for the iPhone/iPod, which works over wifi, not infrared.
Doubtful, as that can only control one device at a time. If the OP says that he pair the Apple TV with his remote then, the Remote app would be set to the Apple TV and not his Mac. Thus, he would not be posting about his remote controlling his Mac after it was paired with his Apple TV.
The IR remote doesn't have to be paired with anything -- it either works or not. OP, what are you talking about?