To answer your original question, the person who owns the router can look at the router's settings and see the devices connected to it. From that table he would be able to see your laptop. However, as was mentioned previously, if the person did not know how to secure his own router, it's doubtful he knows how to look up the devices using it.
As for your second question, it has nothing to do with the router and more to do with the new operating system. In XP, when you look at My Network Places, it fills with the other computers and devices on the network through a feature of Windows called network discovery. On Vista, this feature is turned off by default and can be turned on through your network settings in control panel. Since network discovery was turned off, it did not look for other devices on the network you were connected to and thus only showed the computer you were on. Had the laptop been an XP box, and you had done the same thing, you would have seen all the other computers connected to the router you were connected to.