When does the time prohibiting conversation after Isha' begin: Is it immediately after the Isha' prayer, or after the Witr prayer, or after a person performs any prayer that concludes their day, and what is the intended meaning of the noble prophetic Hadith: "He [the Prophet] disliked sleep before it [the Isha' prayer] and conversation after it"?

There is no specific time legislated for sleeping after 'Isha', rather it depends on what is beneficial. Staying up late after 'Isha' is disliked if it is frivolous and without benefit, due to what might result from it, such as missing the Fajr prayer or the night vigil (Qiyam al-Layl). However, if staying up late is for an act of obedience, such as studying religious knowledge or discussing Muslim affairs, then it is a commendable act of obedience. The Prophet, peace and blessings be upon him, and his Companions stayed up late for such matters. Some of the Salaf (pious predecessors) found it commendable for prayer to be the last action before sleep.