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 having a wet dream during the day in Ramadan break the fast?
Having a wet dream during the day in Ramadan does not invalidate the fast. However, one must perform ghusl (ritual purification) to ensure they do not miss their prayers.
Is the prayer of someone who didn`t face Quibla (Ka`ba direction) valid?
All perfect praise be to Allah,The Lord of The Worlds. Facing the Quibla is a condition for the validity of prayer, and the prayer of the person who hadn`t faced the direction of the Quibla is invalid, and he is obliged to repeat it. And Allah Knows Best.
Should nail polish be removed before making ablution?
Yes, it should be removed because it prevents water from reaching the nails.