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.
What is the ruling on speaking while relieving oneself?
It is disliked for one relieving himself to speak while doing so, except out of necessity. And Allah the Almighty knows best.
Should nail polish be removed before making ablution?
Yes, it should be removed because it prevents water from reaching the nails.
Should one who doesn`t perform prayer out of laziness make it up later, and how should he/she do so?
All perfect praise be to Allah,The Lord of The Worlds He/she is obliged to make up missed prayers by offering with each obligatory prayer another one, and if he/she offers two, then it is better. And Allah Knows Best.
