Good point, GL. For some reason I was thinking the new versions would take precedence. But, how about if it works like this:
When Belthasar chooses to interfere with Kid, he does so by killing her off while she's traveling back in time (we know from playing CT that there's some perceptible time while in a gate). This way, the old Kid would never arrive in 1004 AD. Now when Belthasar sends back Kid from the new timeline, she won't be erased via Time-Traveler's immunity, and we'll get a loop.
There is a small question of why the new Kid isn't erased or killed while traveling by the old Belthasar, but this could be explained by saying she's at the wrong 5-D coordinates since she's traveling from a different timeline, so Belthasar would miss her. She also isn't erased, as time-traveler's immunity only applies within timelines, not while traveling (well, assuming this).
Now, we're back in the same situation of alternating timelines. What might happen is that the two possibilities (Kid succeeding versus Kid failing) alternate infinitely fast, so both timelines exist half the time (also dealing with our conservation of energy problems).
And, in the merged time-line, would this T-2 Kid still pop out in 10XX AD? Would that mean T-2 Kid would still exist after that even if the game's Kid merged with Schala?
I really can't say about what happens in the merged timeline. Perhaps she'll appear, perhaps she won't.
More trivial but, something else which is interesting is that there must be another time-traveling machine beside the Neo-Epoch, as there are 2 time-travelers and the Neo-Epoch can only bear one person (according to Luccia if I recall correctly).
Not necessarily. The Neo-Epoch only needs to carry one person, as only one is traveling for each dimension, with their own Neo-Epoch.