Martyrdom

There are thousands of books on Imam Ali (AS) in many languages and I doubt that you have time to read all of them, but you can read Nahjul Balagha (having some of his sayings and sermons and letters) which is available in many languages including English and try to follow the teachings of Imam Ali (AS). That will change your life to a real successful life.

More information can be found in books like Biharul Anwaar, Volume 31and Kitab al-Irshad by al-Mufeed and Imam Ali from Mahd Ila  Al-Lahd by late Sayed Kadhim al-Qazwini and many other books.

Wassalam.

Wearing perfume has been mentioned in the Hadeeths from the Prophet (SAWA) and Ahlul Bayt (AS) as highly recommended which multiplies the reward of the Prayers seventy folds. This recommended act is for all the time and all situations. It does mean celebration as some cultures take it but it is an act of worship. It is always recommended unless your culture and your community take it as a celebrity which they don't do it in sad occasions.
Followed Islamic teachings is above following our cultures or habits.
Wassalam.

There is no re birth but resurrections or return to this life which known as  Raj'ah رجعة.

Raj'ah is the return of best servants of Allah and worst enemies of Allah to this life again to witness the victory of Islam and the punishment of its enemies. It is mentioned in Quran ( Sura Ghaafir, verse 11).

Imam Hussain (AS) will come back to this life in Raj'ah.

Wassalam.

Imam Hussain (AS) knew definitely that he will be martyred in Karbala and went for his martyrdom because it was the only way to save Islam from deviation and Muslim Ummah from doing astray.

No doubt, Imam Hussain was informed by his grandfather, Prophet Muhammad (SAWA), his mother (SA) , his father (AS) and his brother Imam Hasan (AS) about details of what will happen in Karbala. Allah (SWT) grants His best servants from His knowledge of the Unseen.

Wassalam.

These narrations are in Sunni books.

I did not find them in our authentic Shia books of Hadeeth. We have narrations that the believer will get in the Paradise his believing wife as the most beautiful woman along with the Hoor.

Wassalam.

According to Amaali al-Shaikh al-Sadouq, Janab e Muslim ibn Aqeel (AS) had two sons martyred in the day of Ashura with Imam Husain (AS) and another two sons who ran away from Karbala after the martyrdom of imam Husain (AS). These two sons where martyred later on after Karbala and were buried near Musayyab in Iraq. أمالي الشيخ الصدوق

Wassalam.

Hazrat Abbas (AS) was the chief commander of the army of imam Husain (AS) and he had to remain till the end of the battle.

Wassalam.

Those who were been martyred in the way of Allah are alive ( Sura 2, verse 154 and Sura 3, verse 169). No doubt that the martyrs listen to us when we talk to them. In fact, every dead person can hear us when we talk to him loudly as the Prophet (SAWA) spoke to the dead Kafirs who were killed in the battle of Badr.

Martyrs have real life in which they can listen. Regarding the letters, it depends on the status of the martyr. Letters written to the Infallible Imams will be seen they them and might be even replied, but that is not for every martyr.

'Wassalam.

Yes. Woman can be a martyr in different ways. Mother of Ammar ibn Yaasir was martyred by the disbelievers in Makkah and mother Wahab was martyred in Karbala and any Momina who dies with the love of Ahlul Bayt (AS) will die as a martyr. (Tafseer Al-Zamakhshari , v. 4,  Tafseer Al-Raazi) v. 27.

Wassalam.

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.

This narration المطعون شهيد is found in Sunni books of Hadeeth ( Riyadh al-Saliheen 1:1353 from Abu Huraira) but I did not find it in our authentic books of Hadeeth. It has been mentioned in few of our books of Fiqh but the meaning of مطعون is not a victim of plague but a stabbed person. مطعون can be from طاعون plague and can be from طعن which means stabbing. The meaning of the narration if it was authentic can be a victim of plague or a stabbed to death.

If it is an authentic, it does not mean a real martyr who should not be given Ghusl, but it means the reward which he gets because he was a victim.

Wassalam.