Has it been reported that the Prophet (peace be upon him) recited the beginning of Surat Al-Kahf and the end of Surat Al-Jumu'ah in the Fajr prayer, and if not, what is the sharia ruling on that?

It was part of the Prophet's guidance (peace be upon him) regarding the Fajr prayer to lengthen the recitation. He would recite between sixty and one hundred verses, and sometimes he would recite long surahs such as Surah At-Tur, Al-Waqi'ah, Qaf, As-Saffat, or Al-Mu'minun. When traveling, he might recite Al-Mu'awwidhatayn (Surahs Al-Falaq and An-Nas). On Fridays, he would recite Surah As-Sajdah and Surah Al-Insan in their entirety.

The imam's practice of dedicating specific surahs for recitation in Fajr prayer is an innovation (bid'ah). The correct approach is for the imam to recite whatever is easy from the Qur'an without specification, because specification without evidence is an innovation.

It is obligatory for the imam to be keen on establishing the Sunnah in his prayer with the people. Varying the recitation in Fajr prayer is better and more beneficial for the people, and further from boredom.