All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
With regard to your first question, in fasting in order to make up for missed days, it is a condition that one makes the intention for every day. Making only one intention for making all the days is not sufficient as it is a fasting that does not require continuation.
As for the fasting in which continuation is required, such as fasting for expiating for Dhihaar (from their wives) and the fasting of the month of Ramadan, then one intention at its beginning is sufficient according to the Maaliki School of jurisprudence.
Khaleel said in his Mukhtasar:
“One intention is sufficient for the fasting whose continuation is obligatory.” [End of quote]
It is understood from the above statement that the fasting that is not obligatory to be continuous, like the fasting for making up missed days, it is obligatory to have the intention by night for it for every night.
Manh al-Jaleel reads: “One intention is not sufficient for a continuous fasting that is not an obligation, such as the fasting of the time, or year or month, or week voluntarily without it being a vow, or a particular repeated day, such as every Thursday or every Monday, even if one singles it out with a vow, and every fasting whose continuation is not obligatory, such as making up for the month of Ramadan, an expiation for an oath, or a ransom.” [End of quote]
As for your second question, first of all, we say that the intention is by the heart, and it is not permissible to utter it with the tongue according to the correct opinion of the scholars.
Also, if the Aathaan is called after the beginning of the time of the prayer, then it is valid for you to fast this day as a way of making up for an obligatory fasting, according to the Hanafi School of jurisprudence, because they are of the view that it is permissible to make the intention by day when making up for an obligatory fasting.
But according to the view of the majority of the scholars, it is not sufficient; it is not valid for you to fast this day as a way of making up for an obligatory fasting.
It appears that you are affected with whispers. Hence, it is permissible for you to act according to the view of the Hanafi School of jurisprudence. As regards when the Aathaan is called before the beginning of the time (of the Fajr prayer), then your fast is valid by the agreement of all the scholars.
Allah knows best.