What is the ruling on wiping over socks?
It is not permissible to wipe over most common socks today because the conditions for wiping are not met. The concession was reported for wiping over leather socks (khuff) and socks (jowrab) with conditions: They must be thick, not allowing poured water to penetrate, enable one to walk in them, be worn while in a state of purity (from ablution), cover the entire foot up to the ankles (meaning covering the protruding ankle bones), and not be torn. And Allah the Almighty knows best.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
What is the ruling if a postpartum woman becomes pure before forty days; are acts of worship obligatory upon her, and is she permissible for her husband?
If the postpartum woman becomes definitely pure before forty days, she must perform the ritual bath and perform acts of worship as a pure woman does. What was prohibited for her also becomes permissible, so she becomes permissible for her husband after her bath. The minimum duration for postpartum bleeding is a moment (an instant), and its usual maximum is forty days. Reaching forty days is not a condition; rather, it is sufficient for the blood to stop or to see the white discharge (qassa bayda'). And Allah the Almighty knows best.
Is a person who is in a state of Janabah (major ritual impurity due to having a marital intercourse, ejaculation, menstruation, and post-delivery impurities) sinful if he/she goes about his/her daily life activities in that state i.e. without making Ghusl (ritual bath)?
It goes without saying that a Muslim should always be in a state of ritual purity so as to be able to perform prayers and recite Quran. It is from Sunnah (Prophetic tradition) that a Muslim hastens to make Ghusl from Janabah, but he/she is not sinful in case he/she delayed that provided that he/she doesn`t miss prayers. However, it is permissible for him/her to go about their daily activities while in a state of Janabah, but had better bathe in order not to miss any prayer.