Qadha of Witr, Sunnats and Nafl

Does one have to make qadha of the Witr Salaah if the Esha Salaah was not valid

Q: A person performed his Esha and Witr Salaah on a particular day. Later, he realized that his Esha Salaah was not valid (after the time for Esha and Witr had expired). Should he just perform the qada of Esha (since it was invalid) or should he also perform the qada of Witr (even though he performed witr correctly)?

Making qadha of the sunnats of fajr

Q: I heard from some Ulama or some Book that, we need to pray only Fajr Sunnah Qazaa from all the sunnah mukaidaa and no need to perform any other sunnah-e-muqaidaa, kindly confirm is this correct.

Please explain me in detail why we need to perform qazaa salaah only for the Fajer Sunah and why we do not need to perform any other sunnah mukaidaa because Fajer Sunnah is also sunnate mukaidaa.