Sayyed Mohammad Al-Musawi

Gold is not prohibited in Islam and millions of Muslim women wear gold, but Muslim men are not allowed to wear gold. Every prohibited act in Islam is damagingly harmful. Details of harm and damage are best known to Allah (SWT).

Wassalam.

Muslim should spread useful knowledge among people but we are not allowed to harm others or cause loss to them or violate their rights.

'Wassalam.

Yes it is allowed as far as the company which issued the shares is dealing with fully lawful business.

'Wassalam.

We are not allowed to invest in any company dealing with unlawful activities no matter how much is the percentage of it. Muslim is allowed to invest when 100% of the business is lawful.

'Wassalam.

You should try your best to get your previous pictures ( with out Hijab) and keep them away from  public display. If you could not get all of them, you will not be responsible about them as you were not a Muslim when the photos were displayed. Now when you are a Muslim, it is not sin on you as it is out of your ability to remove it.

Wassalam.

Yes it is Makrouh (Disliked) to sleep between Fajr and sunrise. Many authentic Hadeeths stated that it is recommended to be busy in that time ( between Fajr and sunrise) in prayers, Du'a, remembering Allah, reciting Quran and any useful deeds but not sleeping unless you are unwell or have another valid reason to sleep then. The benefits of being busy in that time in worship are too many including good health and more sustenance. Sleeping during that time might cause a diverse results on health and sustenance according to the Hadeeth. ( Manla Yahdharuhul Faqeeh, number 1439 and 1440)

Wassalam.

Husband is responsible to pay for all livelihood expenses of his wife. This responsibility is part and parcel of the marriage agreement. If he fails to pay for his wife's livelihood expenses, she has the right to ask for all the unpaid expenses which remain as a debt on him. She will also have the right to ask the Marje of Taqleed or his deputy to diverge her if her husband insists on not giving her her livelihood expenses.

'All the expenses of his children is responsibility of their father.

'Wassalam. 

Books of History mention that Hazrat Abul Fazl Al-Abbas (a.s.) had 5 sons. Obaydullah, Al Fazl, Al Hasan, Al Qasim and Muhammad. History also mentioned that he had 2 daughters. Mohammad Ibn Al-Abbas is mentioned as one of the Martyrs in Karbala. 
Obaydullah son of Al-Abbas Ibn Ameerul Mo'mineen (a.s.) is been mentioned as the son who left children. All  the grandchildren of Al-Abbas (a.s.) were from the sons of Obaydullah. The grand and great grand children of Al-Abbas (a.s.) are many and they include many Scholars and very pious believers and very respected personalities in the history of Muslims. One of the well-known personalities from the great grandchildren of Abul Fazl Al-Abbas (AS) is Al-Hamza al-Sharqi who is buried in Al-Midhatiyyah near Al-Hilla in Iraq and the whole area is called after him as Al-Hamza al-Sharqi.
Wassalam.

Yes she can. There is no condition in Adhan and Iqaamah to be given by the father only or any man. Women including the mother can do it as well.

'Giving the name to the child should not ignore the father's wish.

'Wassalam.

The reward of the believers who do good does not depend on the quantity but the quality of worship. Quality of worship depends on the degree of sincerity and dedication to Allah (SWT). Woman during menstruation gets reward for every good deed she does and gets also compensation for the suffering of menstruation. That will make her reward not less that the reward of pious men who do good. There is no question of any discrimination between man and woman in front of Allah (SWT) who created both of them and granted them equal chances and help to do good. 
'Wassalam.

No.
We are not allowed to touch Quranic words or even letters with out ablution. When tattoo is on your body with Quranic words, you must remain always with ablution which is impossible because you need to go to the toilet and sleep etc.

Wassalam.

The Wisdom behind every rule came from God Almighty is to avoid human beings harm and damage and make their life her and hereafter successful . (The Prophet conveys the message from Allah to allow the good acts and to forbid the evils acts) Sura 7, Verse 157.

Allah (SWT) mentioned in Quran : Remember (Prophet) Lut , We granted him  prophet hood and knowledge and We saved him from the people who practiced evil and filthy deeds. (Sura 17, Verse 74).

What wisdom can be more than the Wisdom of Allah?

Wassalam.