Is it true that if a ritually impure, or a menstruating woman visits one who is in confinement, harm will be inflicted on the latter, or her baby?

This is completely wrong and unfounded piece of information.

How is night prayer offered?

Night prayer is offering voluntary prayer after Maghrib and before Fajr (Dawn). As for Tahajjud, it is offering voluntary prayer at night after waking up voluntarily, and for Allah`s sake as He Says (What means): "And pray in the small watches of the morning: (it would be) an additional prayer (or spiritual profit) for thee: soon will thy Lord raise thee to a Station of Praise and Glory!" [Al-Isra`/79]. Offering Tahajjud is better than offering voluntary prayer before going to bed.

Is it permissible to donate corneas to Jordan Eye Bank or all the organs via telephone?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Corneas donation that is carried out after one's death is permissible by the Board of Iftaa'. Because this procedure is highly sensitive, the donation process

should undergoes to an accredited mechanism. And Allah, The Exalted, Knows Best  

A woman went for Hajj while pregnant, gave birth after leaving Arafat, and was unable to perform the Tawaf Al-Ifadah. If she cannot stay until she becomes pure from postpartum bleeding (Nifas) and she is from a distant country, what is she liable for?

 

This woman is advised to leave Mecca in a state of Ihram if the caravan departs. Once she reaches a distance where returning to Mecca is not feasible, she should consider herself in a state of being prevented (Muhsar). She may then exit Ihram, and she is required to offer a sacrificial animal (Blood) at that location. Additionally, she must perform a compensatory Hajj at the earliest possible opportunity. And Allah Almighty Knows Best.