Can you use an External Hard Drive on the new XBox 360 to play old XBox games Ex. Halo 2?

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.