When he recites a verse during prayer he translates the meaning into his language in his mind
(sometimes I say it in my heart.) For example, I would recite the first verse of Surah Fatiha, then after this I would say: "All praise is due to Allah, the Cherisher and Sustainer of the Worlds." Is this right, or permissible?.
There is nothing wrong with it if you recite a verse of the Qur’aan during your prayer and ponder its meaning in your own language, and say that to yourself as you mentioned in the example. This comes under the heading of pondering and thinking of the meaning. That is on condition that you do not utter it out loud, because the one who is praying is forbidden to speak during the prayer, based on the report narrated by Muslim (537) from Mu‘aawiyah ibn al-Hakam al-Sulmi who said: Whilst I was praying with the Messenger of Allaah (blessings and peace of Allah be upon him), a man among the people sneezed and I said: Yarhamuk Allaah (may Allah have mercy on you). The people glared at me and I said: May my mother be bereft of me! Why are you staring at me? They started striking their hands on their thighs, and when I realized that they were telling me to be quiet, (I felt angry) but I kept quiet. When the Messenger of Allaah (blessings and peace of Allah be upon him) had prayed – may my father and mother be sacrificed for him; by Allaah I have never seen a better teacher or better teachings before or since; he did not rebuke me, hit me or revile me – he said: “This prayer is not the right place for any of the people’s speech, rather it is tasbeeh, takbeer and recitation of Qur’aan,” or words to that effect.
And because it is not permissible to recite Qur’aan in any language other than Arabic. See the answer to question no. 3471.
It is permissible in naafil prayers to hold a Mus-haf with a tafseer in the margins or footnotes, and to look at the meaning of what you do not understand. See the answer to question no. 9505
And Allah knows best.