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.

Does passing wind from the anus affect ritual purity?

Ablution is nullified by the passing of wind from the anus, but washing the anus is not required as wind leaves no impurity.

Is it permissible to thin the eyebrows or remove them and draw in their place?

Thinning the eyebrows, removing them, and drawing in their place—known as Namas—is prohibited. The Prophet (peace be upon him) cursed those who do it. And Allah Knows Best.

Is it permissible for the person who wants to travel from the United Arab Emirates to Jordan during the daytime in Ramadan to break his fast before leaving his country; knowing that he had embarked on journey half an hour after dawn?

Praise be to Allah the Lord of the Worlds.

The person who made the intention to embark on journey after dawn must observe fast for that day, because it became an obligation on him before engaging on journey. However, if he experienced unbearable hardship while on travel, then he is permitted to break his fast, but he must make up for the missed day. And Allah The Almighty Knows Best.