What is the ruling on shaving one`s beard?

All Perefct Praise is due to Allah The Lord of The Worlds.

Growing a beard is an obligation and a Muslim shouldn't do otherwise, besides; what is obligatory in Islam shouldn't be violated save for a necessity. And Allah Knows Best.

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 permissible to abort my embryo if there was a risk on my Life?

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                                                                                                                                                                                                                            Abortion is permissible if it was confirmed that the existence of the fetus within his mother's Belly might cause her certain death.Therefore, abortion is permissible if the above conditions were met. And Allah Knows Best.

Is it permissible for one to give the Zakah (obligatory charity) to his indebted brother?

It is permissible for one to give the Zakah to his brother if he was indebted, or poor.