Is it enough to say Tasbeeh (Saying Subhaana Rabbiya Al-‘Atheem during Rukoo`, and saying Subhaana Rabbiya Al-A‘laa during Sujood ) once, or twice during Rukoo`(Bowing in prayer) and Sujood (Prostration)?
All perfect praise be to Allah, The Lord of The Worlds Yes, saying Tasbeeh once during Rukoo` and Sujood is enough, provided that the worshiper`s attentiveness of the heart isn`t undermined during each. As regards the recompense, it depends on the number of Tasbeeh. And Allah Knows Best.
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.
If a disposable water bottle has the logo (Al-Aziz Water Shop) ,is it allowed to throw it away considering that (Al-Aziz) is one of Allah`s beautiful names?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
You can remove some of the letters so that the word isn`t read as (Al-Aziz). And Allah The Almighty Knows Best.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.