What is an "Emergency Call," and can I  set number for it?
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.