Is it permissible to perform the prostration of recitation (sujud at-tilawah) during times when prayer is prohibited, such as: after the Asr and Maghrib prayers, after the Fajr and sunrise prayers, and after the Witr prayer?

It is permissible to perform the prostration of recitation (sajdat al-tilawah) after the Witr prayer, because the time after Witr is not a time when prostration is forbidden. The correct view is that performing voluntary prayers after Witr is permissible. If voluntary prayers are permissible, then the prostration of recitation is permissible even more so, as it is allowed even during times when voluntary prayers are otherwise prohibited.