Is there an authentic Hadith that mentions that the reciter of Al-Fatihah and the last part of Surat Al-Baqarah is granted a reward for every letter thereof, and what is this reward beyond the multiplication of a good deed tenfold for reading a letter, and is the text related to supplicating with these verses?

The hadith you mentioned is authentic. It is narrated from Ibn Abbas, may Allah be pleased with them both, that Jibreel informed the Prophet, peace and blessings be upon him, of the descent of an angel who had never descended before that day. The angel gave him glad tidings of two lights that no prophet before him had been given: the Fatiha of the Book and the concluding verses of Surat Al-Baqarah. The angel also stated that nothing from these two (lights) would be recited but that it would be granted to the reciter. Scholars have differed concerning the meaning of "it would be granted to him." Some understood it to mean that the supplicant would be given what he prayed for, while others understood it to mean reward. Some combined both meanings, saying: if the verse is a supplication, like "Guide us to the straight path," then the supplicant is granted what he asked for. If it is praise and glorification, then its reward is granted.