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.
Someone wiped over his shoes after wearing them in a state of purity, then took them off and prayed without them?
Ablution is not invalidated by taking off leather socks or shoes after wiping over them. However, whoever takes them off after wiping must wash his feet only. If he prayed without washing his feet, he must wash his feet and repeat the prayer. And Allah the Almighty knows best.
Does touching women temporarily forbidden in marriage nullify ablution?
It is prohibited to touch, or to shake hands with such women as they are considered strangers, and doing so nullifies ablution.
What type of illness that permits breaking the fast in Ramadan?
It is an illness that, if one fasts, there is a fear it may lead to their death or cause unbearable hardship.