Playing OG Xbox games on Xbox360

Hi, I haven't found the exact clarification for this case, so asking here.

1. Can you play OG Xbox games on physical discs on Xbox360?

2. If yes, are all games from THIS LIST backwards compatible also via phycial discs or only digitally?

3. I've read playing backward compatible DIGITAL games require buying HDD that is specifically original Microsoft one. Does playing PHISICAL disc also require buying original HDD?