Is it permissible to supplicate in sujūd during the obligatory and non obligatory prayer in other than the Arabic language?
Supplicating is not obligatory rather it is a sunnah and the correct opinion is that it is permissible. As for if he is proficient in the Arabic language then it is better for him to supplicate in Arabic. However if he is not proficient in it or it is difficult for him and maybe he spends a lot of time trying to put sentences together then he should supplicate with that which he is able and it is not obligatory that it be with the Arabic language. The ruling in this is one whether it be during the obligatory or non obligatory prayer.
Likewise supplicating with that which has been reported [in the Quran and sunnah] or that which has not been reported, then it is all permissible.
And Allah knows best.
Benefited from: Shaikh Abu Abdillah Muhammad Ba Jamaal (May Allah preserve him)
Translated by: Abu Musa Jamaal al-Britani