How many rak'ahs are in the Sunnah prayer before 'Isha, and is it permissible to pray as much as one wishes after 'Isha?

There is no established specific number for supererogatory (nafl) prayers before the 'Isha prayer; the matter is broad in this regard. Rather, one should perform many of them between Maghrib and 'Isha as a means of drawing closer to Allah. Indeed, some scholars have considered these prayers as part of Qiyam al-Layl (night vigil prayer) and they have been named "Salat al-Awwabin" (prayer of the often-returning/penitent). Similarly, one should be diligent in performing supererogatory prayers after 'Isha, especially in the last part of the night, as this was part of the Prophet's guidance (peace be upon him).