obviously,yes
You need to flash the DVD drive and the Xbox firmware.
no
you can not, you need the game disc
Yes, assuming you have a reasonably fast connection (USB 2.0 recommended) you can put the WoW folder on an external hard drive or even flash drive or USB stick and play the game from there.
No you can not download and play PS2 games that way.
No, flv player can just play flash video files, not flash games. You could use Adobe Flash Player to play flash games.
Yes, you can install games on an external hard drive as long as the machine which it is connected to has all of the requirements needed to install/play.
Yes, World of Warcarft will play from an external hard drive. That being said, it probably is not the best idea to actually do it because there will be a lot of long load times starting it, and while playing.
If the drive on the PS2 is broken just buy a used PS2, they are very cheap and many come with games and accessories
No, you cannot use an external hard drive on the Xbox 360 to play original Xbox games like Halo 2. The Xbox 360 is backwards compatible with select original Xbox titles, but these games must be installed on the console's internal hard drive or a compatible Xbox 360 hard drive. An external hard drive can be used for storing Xbox 360 games and data, but it won't support original Xbox game playback.
For Grand Theft Auto: V, there will be an initial install on Xbox 360 that will require an Xbox 360 Hard Drive or an external 16GB USB flash drive with at least 8 GB of free space. If using a USB flash drive it must be at least USB 2.0 with a minimum 15mb/s read speed and formatted for Xbox 360 use. A new USB flash drive is recommended to ensure optimum performance.
There are a few different external disk drives you can get that will play Sims 3. You can try getting the 250g external disk drive.