Is it permissible to recite the stated adhkar in any way that conforms to the Arabic language, and what is the ruling on prolonging the ياء (ya’) in "Rabbī" between the two prostrations, or in the adhkar of rukoo’ (bowing) and sujood (prostration), and prolonging the ص (saad) in "sirāṭ" in the opening supplication (du’ā’ al-istiftāḥ), and changing the word "al-ghuyūb" in the istikhara du’a, and saying "an-nabī’" in the tashahhud?

What you mentioned differs from our situation. The "ya" in the word "Rabbī" (my Lord), if omitted, is not pronounced. If it is affirmed, it is omitted in pronunciation due to the meeting of two silent letters, so the "ya" is not pronounced, but rather a kasra (short 'i' vowel). The rule is that if two silent letters meet, the first one is vocalized with a kasra, unless the first is a letter of prolongation (madd), in which case it is omitted, as is the case here. Thus, the prolongation of "Rabbī" is not linguistically possible in the first place. As for the examples mentioned, such as the different pronunciations of "Jibrīl" (Gabriel), "ghuyūb" (unseen), and "ṣirāṭ" (path), the language permits them, and there is no objection to pronouncing them in any linguistically correct way.