Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?
Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.
Is Zakah (obligatory charity) due on the Zakah money received by a poor person, and reached a Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over having it in his possession?
Yes, the poor who possessed a Nissab for a whole lunar year is obliged to pay the Zakah due on that money even if it was given to him as a Zakah money in the first place. And Allah Knows Best.
What is the ruling on Friday Ghusl (ritual bath)?
Friday Ghusl is a confirmed Sunna (Prophetic tradition) even if a person wasn`t in a state of Janbah (ritual impurity), or physically unclean. However, one who doesn`t make Ghusl on Friday isn`t sinful for the Prophet (PBUH) said: "It is good for a Muslim to make ablution for Friday prayer, but it is better to make Ghusul. [At-Tirmithi & Abu Dawood].
Is my husband entitled to take my salary?
Your salary is yours, and you may give some of it to him as a kind of free-will contribution.