Once you hit Level 60, you can get a flying mount from Orgrimmar or Stormwind (as well as some other out-of-place locations). Ask a city guard for a profession trainer, then ask for the riding trainer.
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Nordrassil is located in the Mount Hyjal zone, or will be when the Cataclysm expansion hits.
You can learn to ride mounts at level 20. To learn the training required, go to your race's home city (ie Stormwind for humans, Sen'Jin Village for Trolls) and talk to the riding trainer. It will cost you about 1 gold. To buy the mount, talk to the mount vendor that should be right next to the trainer, they are cheap. You can learn higher levels as you level. Level 40 for Epic Riding, 60 for Flying, and 70 for Epic Flight. At level 77 you can learn Cold Weather Flying, allowing you to ride flying mounts in Northrend. In the coming expansion, Cataclysm, you will be allowed to fly in the old world.
No, you can not buy my world of warcraft account, i have put too much time and money into it.
Yes, you use your Battle.net account to log into World of Warcraft.
World of Warcraft is listed as compatible with Windows 7, and should work fine.