1) will be tricky, you need a debug bios loaded (which is hard unless you know what you're doing, i'm tryin to get one on as a dual-boot now, that means when i press eject it will load that bios instead of the normal mod) not sure how the rest goes but i think the debug bios is used to dump the memory or something and then you can use the trainer tools, but i really not sure as i never done any of this before.
2) i've used HDDLoader, dvd2xbox and some disc dumping thing. dvd2xbox is by far the best.
3) i have pcsxbox but my dvd drive wont read the discs so yaeh im screwed there, i dumped them on my computer and transferred them to my xbox in a folder. used pcsxbox to load the system file or whatever it is, and it runs the games. ive only tested one game though (harvest moon).
4)ps2 on xbox? whats your question? the xbox hardware isn't powerful enough to run those games if an emulator existed anyway, i think.
5)an application like dvdx2 or xbox media center will let you watch them without the remote. personally if i were you i'd get xbox media center, it has everything!
hope this helps. good luck.