Correct, presuming the Mod Chip used is active. I've seen chips that supposedly could "switch-off" with the flick of a switch (mounted on the outside of the XBox), that would cause the XBox to actu normally, allowing use of XBox live while the mod was off.
I haven't tested it (because I don't have a DVD/R drive or an XBox), but couldn't you use a PC to make a direct (bit-for-bit, not file-for-file) backup copy of an XBox DVD? That would work, though I don't know if any DVD writers can do that.
Very correct. Too many people forget the emulator is created without access to proprietary console data (relying on repeated trial-and-error), and is thus copyright of the programmer, not any game company. Also, International Copyright law, allows for a single legal backup of software, presuming it is legally "tied" to the original.
Wake up, George Lucas... The Matrix has you...