What is an "Emergency Call," and can I  set number for it? On the default lock screen, whether using pattern or pin, there is a button at the bottom which says "Emergency Call". But if I try to call my home number or anything it tells me "That is not an emergency call." What does it let through? Is it only 911? 

Is there any way to tell it to allow a certain set of numbers from the emergency button, like to set a list of emergency numbers such as: 911, Home and Wife? This would seem like it would be very useful, so if someone finds you smooshed on the road, they know these certain people should be called.
Yes, it's limited to emergency numbers.  It depends on your region and probably your carrier which ones specifically.

There's no easy way to change it.  While it's probably possible to hack that mode, I would advise against it.  First because it defeats the purpose of having your phone locked (do you really want someone to steal your phone and call your wife?), second because it might screw things up when you really need it (and you can't exactly test whether 911 is working beforehand), and third because you should have ID with you anyways if you're concerned about this.