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.
What should one who made an intention, at night, to make up for a missed fasting day, but broke his fast on the next day?
One who started making up a missed fasting day, then broke his/her fast without a legitimate reason is considered sinful, and is only obliged to make up for the missed fasting days. And Allah Knows Best.
Is it permissible to repeat the Istikhara (seeking guidance) prayer, and is it a condition that one should sleep after offering it?
All perfect praise be to Allah,The Lord of The Worlds Istikhara is offered once, but it is permissible to repeat it, and sleeping after offering it is not a condition for its validity. And Allah Knows Best.
After I was ran over, I had cracked ribs, concussion, a tension pneumothorax, and retired as a result. What is the amount of the Diya?
All praise is due to Allah the Lord of the worlds. May the blessings of Allah be upon our Master and Prophet Muḥammad and his pure progeny.
What you have mentioned requires a detailed medical report since the benefit of every organ that you have lost deserves a full Diya (In Islamic law, Diya is the financial compensation paid to the victim or heirs of a victim in the cases of accidental murder, bodily harm or property damage). Moreover, the decrease in the benefit of some organs has to be assessed by expert doctors and allocated a percentage from the Diya accordingly. Therefore, we advise you to refer the matter to the courts or reconcile with the driver and forgive him so that Allah may forgive you. And Allah The Almighty Knows Best.