What are the supplications after the opening takbir, and is there seeking refuge with Allah (ta'awwudh) or saying Bismillah before Al-Fatiha, and are these repeated in the second rak'ah?

It is prescribed for the worshipper to recite the opening supplication (Istiftah), seeking refuge (Ta'awwudh), and Bismillah after the takbirat al-ihram (opening takbir). The majority of scholars hold that seeking refuge is exclusive to the first rak'ah, while Al-Hasan, 'Ata', Ibrahim al-Nakha'i, and the Shafi'is believe it is desirable in every rak'ah, citing the general meaning of the verse: "So when you recite the Qur'an, seek refuge with Allah from Satan, the expelled." However, the more cautious approach is to limit oneself to what is authentically reported in the Sunnah, which is to seek refuge only before the recitation in the first rak'ah, as indicated by the hadith of Abu Sa'id Al-Khudri. As for Al-Fatihah, one begins with the Bismillah every time it is recited, sometimes vocalizing it and sometimes saying it silently.