What is the ruling on a congregant (ma'mum) secretly supplicating after the audible recitation and before bowing in the Fajr prayer, and what is obligatory and most proper in that regard, and what is the ruling on obligatory prayer with a latecomer (masbuq)?

According to the Malikis, Qunūt is recommended in the second rak'ah of the Fajr prayer, silently after the recitation. It is valid with any supplication, but it is recommended to use the wording: "O Allah, we seek Your help and Your forgiveness..." or "O Allah, guide me among those You have guided...". Similarly, the wording of Qunūt is not fixed for the Shafi'is and Hanbalis; it can be performed with any supplication or a verse containing a supplication. Therefore, your silent supplication while the imam recites the Qunūt silently is valid and recommended.