Does an oath take effect if one swears by other than the three letters of oath (ta, ba, waw), such as by saying: "Ta-Rahman" or "Fa-Allah" or simply "Allah"? And is his covenant with Allah considered an oath even if he did not intend it for obedience or drawing closer to Him?

The letters of oath are three: ba (ب), waw (و), and ta (ت). The letter ta (ت) is exclusive to the name of Allah (lafz al-jalalah), and is not valid with any other names. An oath by "ta-Rahman" (by the Most Merciful), for example, is not valid. As for saying "Allah" without a letter of oath, there is a difference of opinion among scholars; Ibn Qudamah considers it a permissible oath because it is mentioned in the Sharia, while Al-Shafi'i holds that it is not an oath except by intention. The phrase "covenant of Allah" (عهد الله) is considered by many scholars to be a binding oath. In our view, it is both an oath and a vow if one commits to it as an act of nearness (qurbah) and obedience. If it is not an act of nearness, then it is only an oath.