Aya, upon giving Davina the spell to resurrect Kol Mikaelson, states that The Sisters are the only witches in the world with the ability to resurrect people. However, this is not true as both Bonnie Bennett and the Ancestors themselves have been shown with the capacity to resurrect on many occasions. However Aya was exaggerating to impress Davina.
It is possible that somehow, Kol does not retain his ability to practice magic. This, however, does not explain Davina's actions although its been speculated that since she was shunned Davina couldn't use her magic among the Ancestors.
In I'll See You in Hell or New Orleans, Aya states that she is three-times Marcel's age, this would mean that she is around 600 years old. However, in Dead Angels, it is revealed that Aya was the first member and co-founder of the Strix, and that it had been over 900 years since she had last seen the Strix's rule book. There is an indifference of age of over 300 years.
Kol states that Davina and each of the Sisters are linked, and that if he subdued her, the rest would be subdued. This seemed to be correct, however, if the link works like that, when one Sister dies, all sisters should die. Meaning that all the Sisters should be dead due to Ariane's death. However there seems to be a loophole around that since The Strix wouldn't lose their coven all at once.
Davina stated that the originals died with vampire blood in their system, which is wrong since they were the first vampires in history, Esther made them drink doppelgänger blood and cast the spell. However it could because of Davina speculating that since she doesn't know the exact details of the story.