The regular sunnah prayers that are offered before an obligatory prayer must be done after the time for the obligatory prayer begins.

Qiyam Al-Layl is a confirmed Sunnah. Qiyam Al-Layl plays a great role in strengthening one's faith and helping one to do good deeds. Allah praises those who have faith and are pious for their noble characteristics and good deeds, one of the most special of which is Qiyam Al-Layl. It is one of the means of avoiding the punishment of Hell and attaining Paradise. The Prophet said: “The best prayer after the obligatory prayer is prayer at night.”

If offering Duha prayer will not affect the work for which you are responsible, then there is nothing wrong with offering the prayer.

If you fast the tenth and eleventh of Muharram with the intention of making up missed Ramadan fasting, that is permissible and will make up for two of the days that you owe.

If istikharah has to do with an immediate matter that cannot be delayed until the time when prayer is not allowed is over, then it may be done. If istikharah is for something that may be delayed, then it must be delayed.

There is no Sunnah prayer after Fajr prayer. Before Fajr there is a Sunnah ratibah prayer (established Sunnah) which is two rak`ahs.