Read the info on the left hand side when you first run the game. 



If it's possible, try plugging the RJ45 cable from your Internet modem directly into your PC.
It's either a problem with your install of WoW or more likely your Router.
You could try disabling windows firewall. Attempt to connect and play wow and see if it works. From the screens you have provided it looks like some traffic is getting through (you managed to authenticate and see the server browser) and not others.
Remember to re-enable the firewall.

My pc is located next to my router so it is using the Cat-5 Cable
Will it be some settings within the router i need to change?
Yes.
Peer to Peer seems to drain your bandwidth more, so I never use it now.
Note: I'm actually not 100% sure this is the case, I use Vuze to download some stuff via torrents and have no problems whatsoever, so I think the WoW launchers Peer-to-peer technology is dodgy.
I have been thinking of starting playing this for while but before that I would like to know why this game is so addictive. I heard some stories about people leaving things to play this game. I just can't understand why they would do such a thing.
There's nothing dodgy about the blizzard patcher at all, except you can't limit your upload speed without external programs. This is the issue you are having, because it will saturate all your bandwidth using most if not close to all your upload capacity.
Using 3rd party programs of course will have a benefit in performance, vuze and utorrent for example have the ability to limit your upload speed right from the get go.
I have been thinking of starting playing this for while but before that I would like to know why this game is so addictive. I heard some stories about people leaving things to play this game. I just can't understand why they would do such a thing.

I have been thinking of starting playing this for while but before that I would like to know why this game is so addictive. I heard some stories about people leaving things to play this game. I just can't understand why they would do such a thing.