way to go with the spoiler alert
tale of two heads talking, is mentioned in the last codex, so now is canon.
but yeah, the DA have a very long and twisting history.
i have not looked into the religious aspect of the DA so cant comment.
but my own opinions (i am quite vocal on them TBH) on the DA is that luthers men are the green DA and the black 'fallen' are the lions men. t'chulka seeing the lion at odds with his father/brother (as luther was both), did what it thought was best for him and removed the marines loyal to the lion. leaving the calibanites on what was left of caliban (alduruch, tower of angels) to later cover up the failings of their primarch and kill anyone who knew the truth.
t'chulka was a warp engine capable of matter transferance/teleportation over great distances and with ease, it easily moved an entire fleet in the blink of an eye (the lion). this may be the reason for the deathwings use of teleportation tactics.
the current art on DA shows the mechanicum creatures (they may be adepts in the shape of watchers, or watchers, or just adepts) tending to an unknown sperical object, this may be part of t'chulka as it was described as being more in the warp than in real space, there may have been access points created other than the main t'chulka device (which was large enough to need a facility and ate people at an alarming rate