A laptop is a PC.
You don't need a desktop PC to configure a router, you can use a laptop to do so,
by connecting to the router via a network adaptater - either via wifi or ethernet.
Both ways of connecting are included on laptops nowadays.
If you do have a wireless router on, you don't need any other computer to be on, say if you have a laptop downstairs, and a computer with the router upstairs, the computer can be off, but the router has to stay on, and you can access the internet using the laptop from downstairs, if you have a good enough signal. Hope this helps!
For Every Wireless Modem router you need what's called a usb wireless adapter. It will work for every laptop but I'm not sure bout a desktop but buy one that has 2gb or more.
Yes.
The WEP key is the encryption code needed to access a wireless router.
Yes, you can definitely work in any room in the house if you have a wireless router. You can move that laptop all over the house and keep a strong signal.
You need a lan cable (cat-5 should work) does not matter shielded or not. Such cable I believe you can find any computer store.
You need to make sure that your wireless adapter supports the security. Check if the network requires WPA2, if does and you cannot connect to it, it means your adapter can't work with and the router has to configured to work with first generation of WPA.
Any laptop manufactured during the past five to ten years will have an 802.11 b, g, or n wireless interface. Any standard 802.11 b/g/n wireless router will work with any b/g/n laptop, but you may wish to use your computer's Device Manager to see which type your laptop has since you may not want to buy a more expensive 802.11n router if your laptop can only use 802.11b speeds.
Yes.
no
Wifi router does not require internet to function properly, but if you want to have wireless internet you need an internet provider.
No. You need a wireless router, though you don't necessarily need a computer.