Is it obligatory to alert someone who makes a mistake while reciting the Quran? And is not alerting them considered a distortion? And what is the ruling on writing "وآباؤكم" (wa aba'ukum - and your fathers) as a single word?

The mistake in recitation must be corrected if it changes the meaning. And writing {وآباؤكم} (wa ābā'ukum - and your fathers) as one word is correct, not as the questioner assumed, because the conjunctive waw (و) is not separated from the word it conjoins in the Qur'anic manuscripts, and it is not permissible to pronounce the conjoined word without the waw. This is also what has been adopted by the Arabic Language Academies.