Battle of Karbala

Books of History mention that Hazrat Abul Fazl Al-Abbas (a.s.) had 5 sons;

1. Obaydullah, 
    2.    Al Fazl, 
    3.    3. Al Hasan, 
    4.    4. Al Qasim and 
    5.    5. Muhammad. 
    6.    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 Momeneen (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 Momeneen and very respected Personalities in the history of Muslims. Of the well-known personalities from the great grandchildren of Al-Abbas is Al-Hamza who is buried in Al-Midhatiyyah near Al-Hilla and the whole area is now is called after him as Al-Hamza.     
Wassalam.

Some of the martyrs were like that before Karbala like Zuhair ibn al Qayn who was previously a supporter of Othman ibn Affan, but after listening and following Imam Hussain (AS), he believed fully in Ameerul Mo'mineen and Imam Hasan and Imam Husain (AS), that is why he sacrificed his life in the way of Allah under the divine leadership of Imam Husain (AS).

Wassalam.

Human beings have their own ways to express their feelings of grief and sadness as well to express their feelings of happiness. Islam allows different ways of expression of feelings as far as it does not contradict a clear ruling of Islam. No one can express his happiness by dancing, simply because dancing is forbidden in Islam. No one can express his sadness by drinking beer or alcohol, simply because drinking alcohol or beer is forbidden in Islam.

People whom you mentioned in your question are expressing their feelings of grief by their own way which does not contradict with any Islamic clear rule, and does not have bad effect on the image of Islam.

Allah (SWT) grants people the reward according to their intentions. These people are observing and remembering the tragedy of Karbala. May Allah (SWT) grant them reward according to their intentions.

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.

According to Ibn Tawoos in al-Iqbal, the wife of Hazrat Abbas, Lady Lubabah Bint Obaidullah Ibn Abbas, was in Karbala and she witnessed the tragedies and was taken as captive with other ladies and children of Ahlul Bayt (AS) to Kufa then Shaam. She was crying day and night in the tragedies of Karbala and passed away in Madina shortly after returning back. Her children were then looked after by their grandmother Lady Ummul Banin.

'Wassalam.

Allah (SWT) does not enforce justice in this life stopping people from doing wrong, but He gives freedom and leaves human beings to select their own options, whether good or bad, although He guides and helps them to do good, that is why He did not stop Cane from killing his brother Able and did not stop the criminals who killed prophets like Yahya (AS) and did not stop Ibn Muljam from killing Imam Ali (AS). That is the Justice of Allah which gives every one the result of his own actions. 

Wassalam.