1. It depends on where you are. It's illegal in some places but not in others. But whether or not it's legal where you live, if you're asking then you know its not right, right?
2. Depends on their knowledge level and interest in checking. You have to go specifically look.
3. Its in the logs. I have an old 802.11b router that I leave on and unsecured but not connected to anything just to see how many people try to connect to it. All I get is a MAC address and the computer name. That doesn't always tell me anything, but when I see Natalie-PC in the logs, it narrows it down a bit. Which is to say that I've had my share of people try, so my real router is a bit more secure.
4. It depends on the equipment being used, but generally not too far away. See the chart in answer 5 for ballpark figures.
5. Again, it depends on the equipment being used. You can see a chart here
that gives the theoretical maximum distance for the different wireless standards, but those are all under ideal conditions. And I'm sure that anyone with the skills to modify their router to exceed the specs would have their wifi secured.