Is the prayer of a father valid when performed in congregation with his family, despite his inability to recite the Qur'an proficiently and his recitation being without tajweed? And is it obligatory to repeat a silent prayer that a follower has prayed individually after praying it behind his imam?

Not every mistake in reciting Al-Fatiha invalidates it or invalidates the prayer. Reciting it without observing the rules of Tajweed (definition) does not invalidate the prayer, nor does a linguistic error (Lahn) that does not alter the meaning, such as pronouncing the letter "ن" in "الرحمن" (Ar-Rahman) with a Damma (ضم), or the letter "م" in "الرحيم" (Ar-Rahim) with a Damma, or not extending the necessary madd (elongation) in "ولا الضالين" (walad-dallin). However, a linguistic error that changes the meaning, such as pronouncing the letter "ت" in "أنعمت" (An'amta) with a Damma or Kasra, or omitting a letter from Al-Fatiha, invalidates the prayer. If the father's recitation makes the prayer valid, then there is no problem. Otherwise, he should not lead others in prayer, and he should be taught the correct recitation gently and wisely.