All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
It is permissible not to say the Isti’aathah [i.e. saying ‘A’oothu Billaahi min Ash-Shaytaani Ar-rajeem ("I seek refuge in Allaah from the cursed devil") before reciting Chapter Al-Faatihah in the two last Rak’ahs (units of prayer) because the Isti’aathah is desirable and not an obligation. Many jurists are of the view that it is desirable only in the first Rak’ah.
As regards Al-Basmalah (i.e. saying Bismillaaahi Ar-Rahmaani Ar-Raheemi ("In the name of Allaah, the Most Gracious, the Most Merciful") then you should be keen on reciting it because the preponderant view in our opinion is that it is an obligation for the person who is led in prayer to recite Al-Faatihah if the prayer is silent [like Thuhr, and ‘Asr], or that it is a loud prayer [like Fajr, Maghrib and ‘Isha] but the person led in prayer does not hear the recitation. The Basmalah is a verse in Al-Faatihah and the prayer is void without reciting it as per the view of many scholars.
For more benefit, please refer to Fatwa 86155.
If you are unable to complete the recitation of Al-Faatihah behind the Imaam and he bows down before you complete its recitation, then it is an obligation upon the person led in prayer – according to the view we adopt here in Islamweb – to follow his Imaam so that he joins him while he is still in the bowing down position even if he does not complete the recitation of Al-Faatihah, and this is the view of the majority of the scholars.
This is because following the Imaam is an obligation without any difference of opinion while reciting Al-Faatihah for a person who is led in prayer is a matter upon which there is a difference of opinion among the scholars whether or not it is an obligation. Nonetheless, some jurists are of the view that the person led in prayer should complete Al-Faatihah even if he is late in joining the Imaam and he should prostrate after completing its recitation.
Allaah Knows best.