Is reciting Al-Fatiha silently, and raising one's hands after finishing the recitation of the Quran and before the Friday Adhan in the mosque, a correct and obligatory matter, and is it necessary to raise the hands as in supplication (Du'a)?

What the reciter does by raising his voice with the Quran in the mosque before the Friday sermon, and saying "Al-Fatihah" upon finishing with raised hands, is not legislated. It is an innovated matter that the Prophet (peace be upon him) and his Companions did not do. It contradicts his saying (peace be upon him): "And let not some of you raise their voices over others with the Quran," and it causes disturbance to those praying, and there is a risk of falling into showing off. Reciting Al-Fatihah silently or audibly with raised hands after finishing the recitation is also an innovated matter. The Prophet (peace be upon him) said: "Whoever performs an action that is not in accordance with our matter, it will be rejected." So, do not participate with them in this innovation.