Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
What is the amount of food to be given to a needy person for fidyah and kaffarah?
The amount of food to be given to a needy person is 600 grams of wheat or rice.
According to the Hanafi school, it is permissible to give the monetary equivalent instead, and this is the ruling issued by the General Iftaa` Department.
What is the ruling on one who performs ablution or the ritual bath while having nail polish?
Nail polish must be removed before ablution or ritual bath so that water reaches what is beneath it, because it is a barrier that prevents water from reaching that area. This is based on the hadith narrated by Ali (may Allah be pleased with him) from the Prophet (peace be upon him): "Whoever leaves a hair's breadth of his body unwashed from major impurity, such and such will be done to him in the Fire." (Reported by al-Bukhari). And Allah the Almighty knows best.
What is the ruling on performing dry ablution (tayammum) on a wall or stone?
One of the conditions for tayammum is that it be with pure, clean dust (soil). It is not valid to perform tayammum by striking stones, a wall, sand that has no dust (i.e., that does not produce dust), pebbles alone, or clay, as these are not from the earth or its same category. And Allah the Almighty knows best.