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

1. Qiyam al-layl means spending the night, or part of it, even if it is only one hour, in prayer, reading Quran, remembering Allah (dhikr) and other acts of worship. 2. Tahajjud means specifically praying at night, and some scholars limited it to prayers that are offered at night after sleeping. 3. Taraweeh refers to qiyam al-layl in Ramadan at the beginning of the night, which should be made light and not lengthy. It may also be called tahajjud or qiyam al-layl.

The Hadiths indicate that it is permissible for the one who is observing a voluntary fast to break it especially if he is invited to eat by a Muslim.

According to the majority of scholars, the 4-Rak`ah Sunnah prayer should be performed in sets of two, with Taslim after every two Rak`ahs. This ruling is based on the Hadith where the Prophet said, "The prayers of the day and night are to be offered two by two."

The time for Witr prayer lasts from after `Isha’ prayer until dawn begins. Once dawn begins, the time for Witr is over, based on the words of the Prophet: “Pray Witr before morning comes.”

All the ways of offering Witr prayer have been mentioned in the Sunnah, but the best way is not to stick to one particular way; rather one should do it one way one time and another way another time, so that one will have done all the Sunnahs. For more about how to pray witr, see the detailed answer.