Must one who broke her fast in Ramadan, thinking the Maghrib prayer call had sounded based on her father's word and her relatives' confirmation, make up for that day or offer expiation, given that the same thing happened on another day when she ate suhoor after the first call to Fajr prayer based on her mother's word?

There is no sin upon you for breaking your fast if the mistake was not clear to you, and no compensatory fast (qada') is due from you unless the error became apparent to you. This is based on the narration of Umar ibn al-Khattab (may Allah be pleased with him) when he broke his fast, thinking the sun had set, but then it became clear to him that it had not. He said, "The matter is light, and we exerted our effort."

As for eating after hearing the Fajr adhan, there is nothing upon you if the muezzin was calling the adhan before the actual time, because what matters is the appearance of the true dawn, as Allah Almighty says: ﴿And eat and drink until the white thread of dawn becomes distinct to you from the black thread [of night]﴾ [Al-Baqarah: 187]. If you doubted the adhan coinciding with the entry of the time and the doubt persisted, your fast is valid, because the default assumption is the continuation of the night. However, it is preferable to make up this day as a precaution.