Must one who drank after the second Fajr call to prayer in Egypt make up the fast, based on a sheikh's fatwa that the call to prayer is a quarter of an hour before the true dawn, and is she sinful for that?

A Muslim must be cautious and scrupulous regarding doubtful matters, and refrain from eating and drinking when there is doubt about the adhan (definition). If someone ate doubting the rise of dawn, and their doubt persisted without clarification of the situation, then their fast is valid and no compensatory fast (qada') is required according to the majority of scholars. However, it is preferable to make up that day as a precautionary measure and to avoid the disagreement of those who made it obligatory to abstain when in doubt and required a compensatory fast.