Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram (Marriageable) to her.
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.
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.
Are school exams a valid excuse for breaking the fast in Ramadan?
School and university exams are not considered a valid excuse for breaking the fast, as most students take their exams while fasting without experiencing extreme hardship. Fasting does not conflict with exam preparation, and a Muslim seeks strength in obedience to Allah for both worldly and spiritual matters.