Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?
The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).
What is the ruling on wiping the white area behind the ears instead of wiping the head?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. Wiping the white area behind the ears suffices for that. And Allah the almighty knows best.
What is the ruling on one who doubts washing a limb before or after finishing ablution?
If a person performing ablution doubts leaving the washing of a limb from the limbs of ablution during his ablution, he must repeat washing that limb and wash what comes after it. If he doubts leaving the washing of a limb after finishing the ablution, there is nothing upon him. And Allah the Almighty knows best.