The narration about not plucking the eyebrows is from Abu Hurayra, who even was accused by 'A'isha of narrating things that weren't true. He is rejected by Shi'i scholars due to his unreliability. Hence, there is no narration in Shi'i sources about women not being allowed to pluck their eyebrows.

Bismihi Ta'ala

It is obligatory (wajib) to perform the ritual shower (ghusl) after intercourse. The ghusl made is called Ghusl al-Janabah. It does not necessarily need to be immediately after copulation, although it is makruh to do certain things in the state of Janabah, like eating or sleeping. You will also not be able to perform your prayers until you remove yourself from the state of Janabah. This is why it is best not to delay the ghusl for no unnecessary reason.

Bismihi Ta'ala

This indeed is a sad issue that seems to never be solved. The earliest of Shi'ah scholars have addressed this in detail, establishing the completeness and perfection of the Quran, being the everlasting miracle of Islam. 

Books have been written, detailed extensive research has been made, and statements so ever frequently given, all explaining the position of Shi'ah Muslims regarding the holy Quran. 

Bismihi Ta'ala

This question is very broad, and I would firstly recommend that you do some reading on the background of Khums and its rulings. 

A very brief reply to your two questions:

1. What items is khums compulsory on: (1) savings at the end of your khums year, and (2) items that you own but are new and have not been used all the way until the arriving of your khums day. 

2. How should it be distributed: To be given to the office of your Marja' Taqleed, or his shar'i representative (wakil). 

Bismihi Ta'ala

This noble verse speaks about the exclusivity of divine love, and how as believers we must be infatuated in God's love, and not in anyone or anything else. Love of God is something that can be intensified, based on the effort a believer puts in their relationship with the Almighty. 

Bismihi Ta'ala

From the Shi'a point of view an Imam is not chosen by people. Even the ma'soom Imam himself does not chose who the next Imam will be. It is something exclusively appointed by Almighty God.

We clearly know that an Imam must have certain characteristics, the most important of them is 'Ismah, which is not something that can be acquired, and it is something endowed by the Almighty.