The other king in play kills tommen. Can the dupe save him?

Nope. Dupes are considered abilities of the duped character. Tommen's text doesn't say which character ability you can't trigger, so you pretty well can't trigger any of them.

I enjoyed this thread.

I don't really like that reason because if that were true, then it should be written the same exact way as Bowl of Brown. If it meant any additionally gained abilities, then it wouldn't be referenced ownership of a singular ability. That is only my opinion though.