Does the ruling of deliberate breaking of the fast apply to one who broke her fast out of ignorance of the seriousness of the matter? And is expiation obligatory for one who broke her fast with water before the call to prayer, thinking it had already been called based on the words of some of her colleagues?

You are not required to offer expiation (kaffarah (definition)) for breaking your fast on these two days, as expiation is only obligatory for breaking the fast through sexual intercourse. As for breaking the fast on the second day, there is no sin in it because it occurred due to deception. And breaking the fast on the first day carries no sin if it was due to an illness from which you feared harm to yourself.