Is it necessary to do qada of fajr sunnah and of witr?
The linguistic meaning of QADA is compensation.
Revelation, quran and Sahih hadith speak of compensation for a single obligatory prayer or a few obligatory prayers which have been missed due to unavoidable circumstances.
Since witr and sunnah of fajr do not fall under obligatory prayers they cannot be compensated. They cannot be made up if you have missed them unintentionally.
Secondly, the reward system of Allah is so beautiful that if a person prays 28 sunnah of fajr in a month and missed sunnah on a random day because of sleep or unconsciousness, Allah willing his reward is written as if he has prayed the sunnah.