Is it permissible to supplicate by saying: "O Allah, so-and-so, may you succeed," or is it more correct to supplicate by saying: "O Allah, may so-and-so succeed?"

The common colloquial forms like "O Lord, may so-and-so succeed" (يا رب يا فلان تنجح) and "O Lord, may so-and-so succeed" (يا رب فلان ينجح) are correct and have the same meaning; there is no difference between them. Supplicating in classical Arabic is safer, but there is no harm in supplicating in colloquial language or a non-Arabic language, for Allah knows the intention of the supplicant and answers him. Sheikh al-Islam Ibn Taymiyyah mentioned that Allah accepts the supplication of the sincere, whether it is grammatically correct or incorrect, and that striving for grammatical correctness may diminish devotion, and that the essence of supplication lies in the heart.