Word of God said, much to my surprise, that you do need lyrium to use Templar abilities. I suppose that Alistair could use them without it because he had some lyrium in his blood from the training or took some during DA:O.
Gaider actually said that a
templar can still use the abilities for a long time. Considering Cassandra's young age, it could be possible that, if she started using lyrium, it wouldn't have passed that much time that she can't use
templar abilities.
Plus,
templar suffered from withdrawal if they don't assume lyrium (Alistair is a plothole in this). Why would the Chantry makes one of his men suffer it? Why would Cassandra decide to stop assuming it? Plus, Seekers are knows to (generally) be recruited from elite
templars. How can be a young person like cassandra be considered 'elite'?
Furthermore, we haven't see one
templar that remained in the order (or became a Seeker) that stop using lyrium. Why would cassandra decide to stop using it and stop having those abilities.
Considering the Seekers can be non-
templars (the 'generally' part means that they're not all
templars), I haven't seen a single explanation that could lead me to believe she was a
templar. Unless it'll be stated by Bioware, I'll be lei e she wasn't a
templar.
Cole killed Templars when freeing Rhys. but that is all I am aware of.
I was referring to the investigation about the murders in the White spire. Up to the investigation no
templar was killed.