In regard to the wooden idols, it is also completely possible that both cultures developed the idea independently of each other. There are a few benefits of using a tree trunk instead of stone, for example, wood is easier to carve, for the type of idol they are carving it's easier to find a tree trunk in the right shape than it is to find a rock in the right shape, it's generally easier to transport a tree trunk than it is a large rock and so on.
As for "Xian", it is sometimes used as a short form of "Christian" but it is not very common so it often causes confusion rather than understanding of what the user is trying to say.