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.
What is the ruling on a vowed animal sacrifice?
A vowed animal sacrifice is to be distributed amongst the poor and needy, and neither the vow-maker, nor those supported by him are to eat from it.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.