Answer to 1. If you have your PC connected to the internet via a wireless router, then no, you don't have to have it on to have wireless internet; I use my laptop all the time while our desktop PC is turned off.
Answer to 2. As far as I understand it, Wii will connect to the internet just as the DS does; all it needs is a wireless internet connection, or a usb-internet adapter if you don't have a wireless router; a wired connection would also most likely be faster/more reliable. I'm guessing the routers that are compatible with Wi-Fi for the DS, which can be found here, will be compatible with Wii.
i am thinking of buying a usb adapter but i would just turn my comp on to play wi-fi, but what i dont understand is: how will i use the connect 24 with the wii, i dont want to leave my comp left on all day
Will Nintendo sell a Wi-fi dongle for those people that don't have a wi-fi connection in their house? If they don't how are they going to reach a broader market if they don't think about the situations of diffrent people?