What is the difference between Tahajjud prayer and night prayer, and do they have a particular Witr prayer other than that of Isha (evening prayer)?

Tahajjud and Qiyam-Al-Lail (night prayer) are two words for the same meaning which is offering voluntary prayer at night after sunset, but before dawn break. However, Tahajjud is offered after waking up; whereas, Qiyam-Al-Lail is permissible before sleeping, or after it. Therefore, every Tahajjud is a Qiyam, but not every Qiyam is a Tahajjud. Moreover, there is no specified Witr for both of them, but Witr after Isha is by itself the Witr of Qiyam, and it is a Sunnah to postpone it until after Qiyam if the worshiper thought that he was most probably going to wake up in order to offer it, but if he wasn`t sure of waking up, then he is at liberty to offer it before going to bed as was reported in the Prophet`s Hadith.

Is Iddah (waiting period) incumbent on an old woman whose husband had died?

Upon the death of the husband, Iddah is incumbent on the wife regardless of their age. And Allah Knows Best.

Is keeping money in and taking profits from the Islamic Bank lawful? 

If Allah Wills this is lawful, because they stipulate on theselves to work in accordance to the guidlines of Islamic Law. And Alalh Knows Best.

Is it permissible for the heirs of the person who caused the accident (The Killer) to fast (The intended as an expiation for unintentional killing) on his behalf if the latter died in the crash?