So my x360 was banned from live, and now I wonder whether it would work if I download the demos with a friends console to my harddrive (using my gamertag) and then try to play it on my banned x360 at home?

Is there any other alternative way I could try?

And one more thing, if I buy a new core, is it risky to use the HD with both the banned and unbanned consle. That is, I know it's not a problem to use the old HD with a new core console, but is it possible that the new core console will also get banned if I continue to use the HD on both consoles (savegames???).

Demos should work, failing that get a magazine with demos on

as i understand it, as it stands its only the console itself that's banned and not the hard drive. people have reported that they can take their hd and slap it in another console and all's well
save games will not be an issue, from what i understand from wot c4eva was saying is that they were looking at the CR timings of the discs themselves