Abu Lahab's death and related to Hind bint Utbah (RA)?

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How did Abu Lahab die?

I've read on Wikipedia that Abbas (RA) wife smacked him with something, and he bled profusely.

According to Dr Yasir Qadhi he passed due to a mental illness as he was not able to swallow the news that Muslims were victorious at Badr.

And, how was Abu Lahab related to Hind bint Utbah (RA)? Wikipedia suggests she was her sister in law and Abu Sufyan (RA) was his nephew?

On the 7th year of preaching Islam, the Quraysh imposed boycott on Banu Hāshim & Banu Muṭṭalib and forced them to live in a mountain gorge outside the city. Most of the members of Banu Hāshim had not accepted Islam at that time. Yet they stood by Muḥammad and suffered as much as he did. Abu Lahab was the only member of Banu Hāshim who supported the boycott and did not join his clan. Through a deep sense of animosity, Abu Lahab violated this ‘Arab tradition and took the side of non-Muslim Quraysh clans. Abu Lahab renounced his affiliation with the Hashim clan and remained in Mecca. Soon afterwards, he met his sister-in-law, Hind bint Utbah, and said to her, "Haven’t I helped Al-Lat and Al-Uzza, and haven’t I abandoned those who have abandoned them and assisted their opponents?” She replied, “Yes, and may god reward you well, O Abu Utba

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The first people to reach Mecca with the news of the Quraysh defeat in the Battle of Badr were al-Haysuman and 'Abdullāh ibn al-Khuzā'ī, who bewailed the fact that so many of their chieftains had fallen on the battlefield. Abu Lahab went to the large tent of Zamzam, "his face as black as thunder". Before long, his nephew Abu Sufyan ibn al-Harith arrived, so he called him over for news. A small crowd gathered around the two as Abū Sufyān told his uncle, "The facts are the Quraysh met our enemy and turned their backs. They [the Muslims] put us to flight, taking prisoners as they pleased. I cannot blame our tribesmen because they faced not only them but men wearing white robes riding piebald horses, who were between heaven and earth. They spared nothing, and no one had a chance."

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Someone must know.