New HD II.8 Final Chapter Prologue Trailer

[Sephiroth]

As it can be seen in one of the final scenes of Birth by Sleep, Terra's consciousness was still partly linked to his body, therefore being able to co-exist in both the possessed body as well as the armor for awhile, it also fought with Xehanort in there, but Xehanort still was the dominant one on the surface, even after the memory loss. So not everything was kept within the armor alone. Still, with that, by the end of the day, Ansem was the by darkness engulfed Xehanort nonetheless and not Terra.

Also it is not true that Nobodies have no hearts. Xemnas himself explains it in Dream Drop Distance. Nobodies have a "leftover of the original heart" and the Nobody reproduces the missing rest. It was one of the many retcons from "we remember the feeling of having a heart" to this. Just as Xehanort becoming a Heartless was retconned for his "Xehanort replication plan". Because originally he made himself a heartless "just to investigate darkness easier as he could approach it that way", this was amusingly made meaningless by adding the cloaks that protect from darkness and later with Xehanort's explained plan as, in his Ansem form he used the bootstrap paradox to tell his past self to tell what should happen, teach the time manipulation, et cetera.