is the "master" "special" in any way?
No, except that some sort of pull-up/pull-down resistors should probably be on the network somewhere.
Could we, for the sake of an example, have two peers interconnected (Q.B), say one at my house and one at my neighbors. And if EITHER detected something amiss...
Well, you could. In other words, everyone listens, and sometimes somebody talks. In this example, it would be unlikely burglars would break into two houses at the same millisecond.
could there be three peers on the LAN, not just two
Lots of them, I imagine.
Is it able to endure such an event without problems? Without harm to the electronics?
According to the datasheet, yes.
Can the sending device "see" that a collision is taking place?
I'm not sure about that. But what I would do is send a message, and await some sort of response. If you don't get a response, re-send it. Then I would add a randomizing interval (like TCP/IP does I think) so that both ends don't try to resend at the same moment.
But I don't see any real reason why you couldn't have a master/slave arrangement. Then the master controls who talks when (like a teacher in a classroom). That way everyone doesn't talk at once.
Plus, the master could query (eg. every 1/10 of a second) each slave: "is everything OK?". So the slave could reply "burglars!".
This is safer really anyway, because if the burglars cut the wire (or turned off the power) and you are relying upon the slave initiating the conversation, you can't tell the difference between silence (because the power or wire is cut) and silence because nothing is wrong.