In regards to the mod and Xbox Live, they can be compatible if you're extremely careful. If you've been on Live with a particular hard drive, then you can't go on Live with any other hard drive or you'll be banned, that's one restriction. And you CAN go on Live with the mod installed. If you have an original game in the system, and turn on the Xbox with the little power button then the mod isn't loaded and you can access Live fine. I'm pretty paranoid though, and find that it'd be possible to forget, or have a friend screw it up. So what I do is just uninstall the mod when I want to play online, and then reinstall it when I'm done.
The exploit save is on the hard drive, and I have the right copy of MechAssault lying around. Uninstalling the mod takes around 30 seconds, and reinstalling takes another 30 seconds. There's no danger in getting kicked off of Live, and it's very little hassle.