Yes, it is possible to use a laptop as a wireless bridge for xbox live.
unless you get a wireless adapter, yes
It allows you to connect to xbox live on a wireless network
No, what i did is i took the ethernet cable that came with my xbox, connected it to my laptop, and connected my laptop to the internet via wireless router. The only other way that doesn't involve a wireless adapter for your 360 is to connect your 360 to your computer via an ethernet cable (not sure if you need a router for this but i might as well list it), but the laptop-connect is the "most effecient/cheapest" way, and the adapter-connect is the "best connection/signal" way.
Have wifi connection
It will if you buy the 100 dollar wireless adapter.
You have to purchase a laptop aadapter for free. When you have the adapter you can connect to Xbox live but you have to pay for a Xbox live subscription. However you do get a free subscription.
Search http://www.youtube.com for xbox without wireless adapter and you will see videos on how to do just that.
Yes, your xbox can connect with your wireless router. You must buy the wireless add on for the xbox. If you don't wish to pay $100 for the wireless add on, you can just connect an ethernet cable from router into the xbox.
You need an Xbox wireless adapter.
Firstly, make sure you have a wireless router/modem. The Xbox 360 s, the wireless adapter is built in. For the other Xbox's, you need to buy a wireless adapter. After this, you are ready to sign up for Xbox live.
You cant connect to Xbox Live through your PC. You will need to connect straight into your modem, or either use a Microsoft Xbox 360 wireless adapter to connect through your wireless network.