What is the ruling on istibra' and how is it performed?

Istibra' (cleansing from urine) is recommended. It is for a person to ensure that nothing remains of urine in its passage before performing istinja'. Its method is: to clear the throat (or cough slightly), shake the penis (meaning to pass fingers along it to expel any remaining urine if needed), and walk a few steps to the extent that one thinks nothing of urine remains if walking is needed. Each person knows his own nature best. The preferred opinion is that this differs among people. The objective is for one to think that nothing remains in the urinary passage that he fears will exit later. And Allah the Almighty knows best.

A man insulted the Divine Essence; is it obligatory for him to perform Ghusl?

How should a person who is afflicted with continued major ritual impurity (incontinence of urine, bleeding outside the monthly period) perform ablution?

Such a person should make ablution for every prayer after its due time and after removing impurities from their body and outfit, and should place a fresh diaper whenever needed so as for the impurity not to spread out. They should also perform prayer immediately even if incontinence of urine continued, and should repeat the aforementioned for every obligatory prayer, then perform optional prayer as much as they want.

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.