Doubt in Number of Missed Prayers
It is obligatory to make up for the prayers and fasts that one is sure they missed after reaching the age of shar‘ī puberty. One has no duty regarding doubted ones.

Missed Prayers of Father/Mother
The performance of the father’s missed prayers and fasts, is obligatory for his eldest son. By obligatory caution he should perform his mother's missed prayers and fasts as well.

The performance of the father’s missed prayers and fasts, which are obligatory for his eldest son, will not become obligatory for the latter’s son or brother upon his death after that of his father.

By the eldest son, it is meant the eldest son who is alive when his father dies, even if he is not the father’s first son because the first son died before his father. 

In case father/mother did not perform prayer out of rebellion, to perform their missed prayers is not obligatory for the eldest son. However, caution by performing their qaḍā’ prayer, should not be forgone.