Does the fasting become void by a definitive intention to break it, if the breaking of the fast does not actually occur, and is Qada' (making up the day) obligatory for someone who intended to break their fast to prevent themselves from repeating the prayer, and then repeated it?

Scholars have differed regarding whether the fast of one who intends to break it while fasting becomes invalid or not. The intention to break the fast here means a firm resolve and determination to do so, not merely a thought or a passing whisper (waswasa).

Assuming a firm intention to break the fast, you are permitted to follow the scholars who state that the fast does not become invalid in this case, and you are not obligated to adhere to a specific madhhab (definition).

Therefore, your fast is valid, and you are not required to make up for it. We caution you against repeating prayers due to waswasa; rather, you should disregard it and pay no attention to it.