I have no direct reference to the regulations in effect, but in my opinion, a door translation still works on the status quo. The terminology (recursion, translation, etc.) is clearly based on the idea that The Strange works a bit like an algorithm that operates on the universe itself. However, as in the real world, there is no indication that there is a possibility of time travel: that is, there is no "turning back" or recovery of the state. The "translation function", so to speak, is stateless and only acts on the indicated input: the character (in its current state) and the destination.
Although there may be some sort of recursion that is virtually indistinguishable from the original recursion just a few minutes ago …? 😉
So to answer your questions:
1) the character is translated by his replaced member, so he will result in a being with an intact member equivalent and again in a member with all members.
2) Fading tattoos will likely also translate into an equivalent of Ruk and will appear once again when the character is translated.