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.
How many prostrations of Quranic recital are there, and is it permissible not to offer them while reciting?
There is one prostration for the Quranic recital, and it is a Sunnah for which one is rewarded upon offering it. However, one who doesn`t isn`t punished. Therefore, those who fail to offer it aren`t considered sinful, rather they deprive themselves from the reward.
Is it permissible for a woman to observe voluntary fast without her husband's permission?
A woman is not permitted to observe a voluntary fast (nafl) while her husband is present without his permission.
I`m a pious Muslim woman, but my husband isn`t, what should I do?
You should exercise patience, make supplication that Allah guides him to the straight path, and keep advising him kindly.