Women

You should avoid such gatherings in which sinful acts are done.

Wassalam.

No question of inferiority of women in Islam at all. Fatima (AS) was the lady who was granted the highest rank above all human beings including all the pious men and she is the third greatest human being after her father the Prophet Muhammad (SAWA) and her husband Ameerul Mo'mineen (AS).

Wassalam.

Knowledge and degrees of faith are open for women equally as open for men. Many women are much higher in knowledge and faith than thousands of men. Allah (SWT) Created Fatima (AS) who is higher in her knowledge and faith than all human beings except her father and her husband (SAWA). That proves that there is no gender discrimination at all in Islam.

Wassalam.

Woman is recommended to put her hands separately on the two sides of her chest. That is not folding hands at all. 
Wassalam.

Simply, the Shia narrations are taken from the Prophet (SAWA) through the most authentic source who are Ahlul Bayt (AS) while Sunni narrations are mixture from different sources including untrusted narrators like Abu Huraira who narrated that Prayers is invalid if you see a woman or a donkey or a dog. (Saheeh Muslim , V.4, P.228).

'Some Sunni narrations claim that the woman is like a goat (Al-Qurtobi 15:172).

Wassalam.

Aal e Rasool آل رسول cam mean all the family of Bani Ha him. It can also mean by our scholars all the children and grand children from Ali (AS) and Fatimah (AS). The Purified Ahlul Bayt (AS) are all the 14 Infallible.

Wassalam.

Muslim should not promote revealing clothes because it means encouraging sinful acts. If you have a reasonable possibility that such revealing clothes will be covered with other clothes, like Muslim females who wear Hijab over revealing cloth, then there is no problem in selling it, but if you know that such revealing clothes will be worn in public, then you should take not part in promoting sinful acts. Money earned from sinful acts is not Halal as well.

Wassalam.

Both looking at non Mahram woman with make-up  and mingling with her, are not allowed for Muslim man.

Muslim man should lower his gaze and avoid looking at non Mahram women especially when such looking moves his desire in any way.

Wassalam.

There is no question of gender in-equality nor discrimination in Islam if people understand Islamic rules properly. Allah, The Creator Has Created both man and woman and granted both of them the honor (We have honored the children of Adam (Human beings)(Sura 17, Verse 70).

There are common things among both genders like equal human values and honor, equal rights to life , safety, dignity, ownership, education, etc. Yet, there are gender different functions and responsibilities on man and woman, These different functions initiated its own rules to organize life accordingly. Those different rules are less than 5% of the common rules for both genders.

Injustice on any human being being a man or woman is a sinful act.

Both man and woman will get reward for any good act and both will go to the same Paradise, while sinners men and women will face the result of their sins equally.

Wassalam.

Yes, and it is recommended.

Wassalam.