>Is there a limit to how far that signal can run to the second machine..?
The limit, the total distance from one computer through the switch to another computer, is 100 meters (384 feet) for a 100BASE-TX network, about the length of a football field.
>How can I test the integrity of the lines...?
I test them on my existing network by copying 100 MBytes from one computer to another and measuring the time that it takes (http://duxcw.com/digest/Reviews/Network/dlink/dhn910/dhn910-4.htm).
>How can I ... know I'm RJ 45-ing them correctly?
By reading and carefully following http://duxcw.com/digest/Howto/network/cable/cable1.htm, and then testing them. Larry