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.

What is the ruling on combining prayers at the Musala (Place for prayer) of a shopping center because of heavy rain, knowing that some people come from outside that center?

Praise be to Allah, the Lord of the Worlds.

If there is hardship in going back to that Musala at the time of Asr or Isha` prayers, then it is permissible to combine prayers in twos only (Duhr with Asr and Maghrib with Isha`). Kindly consider calling us. And Allah Knows Best.

Is a woman`s neck an Awrah (private part)?

All Perfect Praise is due to The Lord of The Worlds.

It is an Awrah, and it is forbidden for her to reveal it before non-Mahrams (Marriageable men). And Allah Knows Best.

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.