What are the correct opening supplications (Du'a al-Istiftah) authentically reported from the Prophet (peace be upon him), what is the evidence for them, when are they recited, and in which prayers?

The Prophet, peace and blessings be upon him, is reported to have used several different wordings for the opening supplication (Du'a al-Istiftah). Among them is what was narrated by Abu Hurairah, may Allah be pleased with him, requesting distance from sins and purification of the soul from them. Also, what was narrated by Aishah, may Allah be pleased with her, with the wording "Subhanaka Allahumma wa bihamdika" (Glory be to You, O Allah, and with Your praise). As for the obligatory prayer, what is preserved from the Prophet, peace and blessings be upon him, is "Allahumma ba'id bayni wa bayna khatayaya..." (O Allah, distance me from my sins...) or "Subhanaka Allahumma wa bihamdika...". Other supplications include what was narrated by Ali ibn Abi Talib, may Allah be pleased with him, and by Aishah and Ibn Abbas, may Allah be pleased with them both, concerning night prayer. Also, what some companions like Anas and Ibn Umar, may Allah be pleased with them, said. General wordings can be recited in both obligatory and supererogatory prayers, while the wordings specifically prescribed for night prayer are best used therein. One suffices with a single opening supplication from among the various options in a single prayer.