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They do make custom diff mounts to put C6 stuff into the C5. An 05 C6 would still have a T56, so you shouldn't have to extend your exhaust like the TR6060 swap guys do.
No great benefit for just the base C6 differential when you factor in the cost of the custom mounts since they are only as strong as the C5 diff.
Keep your axles, they are better than C6.
If you mean the traditional concept of a transaxle being both the trans and the rear end? Yes, swappable. There are some fine points based on year but so long as you score the rear C6 cradle with the diff and trans you're good to go with some custom mounts.