Is it permissible to supplicate during prostration by saying: "O Ever-Living, O Self-Subsisting, grant me success," or "provide for me"? And is it permissible to say "O Ever-Living, O Self-Subsisting" in supplication generally? If it is not permissible, are the previous prayers unacceptable or valid?

Al-Hayy (The Ever-Living) and Al-Qayyum (The Sustainer of all existence) are among the beautiful names of Allah, and supplicating with them is permissible in all circumstances. Some scholars have even opined that they constitute Allah's Greatest Name (Al-Ism Al-A'zam). There are authentic hadiths indicating the virtue of supplicating with these two names, among them is the Prophet's (peace and blessings be upon him) statement regarding a man who supplicated with them: "By Him in Whose Hand is my soul, he has supplicated Allah with His Greatest Name, which, if He is supplicated thereby, He responds, and if He is asked thereby, He gives." He also advised Fatimah (may Allah be pleased with her) to say: "O Ever-Living, O Sustainer! By Your mercy, I seek help; correct all my affairs for me and do not entrust me to myself for the blink of an eye." Therefore, supplicating with these two names does not invalidate the prayer; rather, it is permissible and rewarded.