So does that mean that the anapsid condition was NOT the ancestral condition of the amniotes?
Yes. At least, this option is at least as parsimonious as the traditional alternative.
Sounds kind of strange to me because the first tetrapods lacked a t.f. entirely.
Yes, but stranger things have happened in evolution.
The mesosaurs are definately mysterious-why do they seem to appear out of nowhere?
What Mike Keesey said.