It depends on adapter. Nowaday all adapters support wpa security.
Yes, but you may have to manually change the setting in the router to accept 802.11g connections. The Belkin default is the newer 802.11n standard.
As long as your network adapter is for the Xbox 360, It will work fine.It just won't be the same colour.
You don't need one. The PlayStation 3 has a network adapter built in (WiFi). It also has bluetooth built in.
I am not going to say it is impossible for a different adapter to work, just unlikely . The Xbox 360 Wireless Network Adapter was made specifically for that purpose, so it is unlikely that a normal adapter will work if attached to the Xbox as they most likely will not be compatible.
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.
Wireless adapter of G type connect work in N type network. To take advantage of N networks you need to have N type network adapter.
Routers do not require presence of other computers to work. You can have even a single router in your network with no computers connected and will still work.
Yes, but stealing is illegal.
Yes, it will you get driver for your adapter from the adapter's manufacture website.
User level operating systems can work only with one network adapter in the same time. If you are trying to use two you might experience problems with connectivity. Thus if you have only one network adapter connected (either wired or wireless) OS should automatically forward all internet "calls" to the adapter.
Preboot Execution Environment (PXE)
If your laptop is equipped with a USB port (most are) then virtually any USB wireless adapter will work.