Did Muhammad marry his own daughter/niece? 

Muhammad, the Prophet of Islam did not marry his own daughter or niece. He got married to his daughter-in-law who was also his cousin, Zaynab. Talking about Zaynab, She was a skilled tanner and leather worker. She continued working as a leatherworker throughout her life, even when she had money to live a good life. As a person, she was calm but would lose her temper quickly. Before marrying Muhammad, she was married to another man who died in 622. Muhammad had an adopted son, Zayd who was first kidnapped by the slave traders and then sold to the nephew of Khadija who then gifted Zayd as a wedding gift to her husband Muhammad, and later Muhammad adopted him. Around 625, Muhammad proposed to Zaynab to marry his adopted son, Zayd. 

Now, highlighting the circumstance which led to the marriage of Muhammad to Zaynab, he has gone to visit Zayd’s house one day but Zayd was not at home. He happens to see Zaynab in the state of undress and seeing her, he exclaimed to himself, 'Praise be to Allah, who turns hearts around!' Later Zaynab told this incident to Zayd and he got scared. Muhammad was the prophet of Islam. His word is the law and his rage is known to all. Seeing this, Zayd told Muhammad about his willingness to divorce Zaynab as Muhammad admires her. The relationship between Zaynab and Zayd got weakened and later he divorced her in 626. Muhammad then married Zaynab in 627.