What is the ruling on the prayer of the Imam and the congregants if the Imam makes a mistake in recitation by using a word similar in meaning to the correct word, such as saying: "كانوا لنا عابدين" (they were worshipping us) instead of "وكانوا لنا خاشعين" (and they were humbly submissive to Us), and is it obligatory for the congregant to correct him?

It is obligatory to correct the Imam (Fatḥ) in Surat Al-Fatiha, and in other surahs if the error corrupts the meaning. It is permissible if it does not change the meaning. The prayer of the follower is not invalidated by correcting his Imam, and this is prescribed by scholars if the Imam pauses or makes a mistake. The jurists of the four schools of thought have explicitly stated the permissibility of this, and that it does not invalidate the prayer of the one who corrects or the Imam. For example, replacing the word "Khashi'een" (humbly submissive) with "Aabideen" (worshippers) does not change the meaning, and correcting here is permissible and does not invalidate the prayer.