Yes it works on 1.6's, but you can't get resolution higher than 640x480. In interlaced mode, there's overscan. In progressive mode, there's very little overscan, although you still can't fit much more on the screen.
If you have to ask, you probably want home edition.
Having component cables doens't necesarily mean anything..... it's whether or not the device it's connected to can receive a 480p signal. If you're connecting your Xbox to a TV that doesn't support 480p, then you can't use the component cables.
It's best not to mention any illegal software here.....
Do you have a HDTV/EDTV? (Basically, is your Xbox hooked up to something that will receive a 480p signal?) If so, then connect your Xbox to your TV using the composite cables, run gentoox, login and run xbvset. Choose HDTV, then 480p and let it reboot. Connect your Xbox to the TV using the component cables and then run Gentoox. It should display in 480p now.
If your TV won't accept 480p signals, then you'll have to use the composite cables for Gentoox.