My Husband Works as a Diver and most of His Client are non-Muslims. Is his work permissible or not?
There is no harm on his job. And Allah Knows Best.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Am I Permitted to Use Ill-gotten Money given to me from Sorcerer's Sons during during my Mother's condolence?
You are permitted to use this money if you were ascertain that the majority of his lawful money surpasses the unlawful one. And Allah Knows Best.
Is it permissible to distribute the raw meat of the vowed animal sacrifice amongst the poor/to offer it to them in cooked form?
It is impermissible for the vow-maker to eat from the vowed animal sacrifice, rather, he/she should distribute it as he/she had intended upon making the vow, but if the vow was a general one, without any specification then, it is better to give it as raw meat.