You can only play some games if you have the Xbox 360 Hardrive and some console software.
Yes And No, xbox 360 games can't be played on the xbox and only some xbox games can be played on the 360. All of the newer games are made for the 360. But you can Hack both of them and play some Xbox games on the Xbox 360 like Halo 2 for example you can play online with Halo 2 on the Xbox 360.
No you need the hard drive and xbox live to play xbox 1 games
If you are referring to an "older xbox" as the regular xbox, then the answer is no. but if you are referring it as the first models of the xbox 360, then you can play halo 3 or any new xbox 360 games on your Xbox 360.
No, it is only on the old xbox, but you can play some of the old xbox games on xbox 360 and Halo: combat evolved (halo 1) and halo 2 are two of them.
As far as I know, you can play all original XBOX games on the XBOX 360. It may be different for some of the first XBOX games but both Halo and Halo 2 are playable on the XBOX 360.
No Halo is an Xbox 360 exclusive and not made for the PS3
Well it depends on what games. Most games u can play xbox live with 2 people. For example on halo 3 u can play 4 people on xbox live...
Yes, my cousins have an Xbox 360 and they have halo one and two for regular xbox and they play it on their xbox
Only some xbox games are compatible with the 360, for example you can play Halo the original, but you can't play Dead or Alive Extreme Beach Volley Ball. It all depends on the game. And if the games was remade for the 360, the chances are no.
No, you do not need Xbox LIVE to play any original Xbox games. Not all original Xbox games can be played, but Halo and Halo 2 do not need LIVE to be played on the Xbox 360. I just now tried it with my LIVE unplugged and signed in to an offline account and it let me play both of them. The previous answer was a lie, obviously.
Some work like halo 1 and 2
You don't have to update your Xbox to play Halo Reach. Some games like Forza Motorsport 4 and Homefront will make you update your Xbox.