Grading: The report of him (peace and blessings be upon him) praying eight rak'ahs of duha is "sahih", but this particular chain is weak.
Technical note / Defect ('illah): Ayyub bin Safwan (or Ibn Abi Safwan) is "majhul" (unknown); al-Bukhari ("al-Tarikh" 1/ 418) and Ibn Abi Hatim (2/ 250) mentioned him but remained silent about him, while Ibn Hibban mentioned him in "al-Thiqat" (5/ 55). According to al-Bukhari, there was disagreement over this narrator in the chain of this hadith.

Details of the narration: Thus 'Abd al-Wahhab bin 'Ata' (as in this narration) narrated it via Sa'id bin Abi 'Arubah, from Ayyub bin Safwan, from Abdullah bin al-Harith, from Umm Hani (may Allah be pleased with her).

Technical note / Defect ('illah): 'Abd al-Wahhab bin 'Ata' was contradicted by 'Abd al-A'la bin 'Abd al-A'la (see al-Bukhari, "al-Tarikh" 1/ 418, and al-Tabari, "al-Tafsir" 23/ 137). He narrated it with the intermediary "Mutawakkil" between Sa'id bin Abi 'Arubah and Ayyub bin Safwan.

Details of the narration: Sadaqah bin Abdullah narrated it, in al-Tabari 23/ 137, via Sa'id bin Abi 'Arubah, from Abu al-Mutawakkil, from Ayyub bin Safwan, from Abdullah bin al-Harith bin Nawfal, from Umm Hani (may Allah be pleased with her).
Technical note / Defect ('illah): Here the narrator is named "Abu al-Mutawakkil", but we do not know any narrator called Mutawakkil or Abu al-Mutawakkil. The error may be from Sa'id bin Abi 'Arubah, since he suffered from ikhtilat (deterioration of memory) at the end of his life. And Allah knows best.
Grading: 'Abd al-Karim bin Abi al-Mukhariq (who is weak) also narrated it, and there was disagreement over him in it as well.

Details of the narration: 'Ali bin Abdullah bin Rashid narrated it from 'Abd al-Karim bin Abi al-Mukhariq, in al-Bukhari's "al-Tarikh" 1/ 418, saying: Ayyub bin Abi Safwan (the mawla of Abdullah bin al-Harith) narrated to me that Ibn Abbas (may Allah be pleased with him) used not to pray the duha prayer.
Technical note / Defect ('illah): Imam al-Bukhari said that at the beginning of this narration Abdullah bin al-Harith is not mentioned, but at its end it says that Abdullah said: Then Ibn Abbas (may Allah be pleased with him) prayed them afterwards.

Corroborating chains and supporting reports: Sufyan bin 'Uyaynah narrated it, in al-Humaydi (335) and al-Bukhari's "al-Tarikh" 1/ 418, via 'Abd al-Karim bin Abi al-Mukhariq, from Abdullah bin al-Harith.
Technical note / Defect ('illah): Ayyub bin Safwan is not mentioned in this chain.

Reference / Source: Al-Tabari narrated it at 23/ 137 via Mis'ar bin Kidam, from 'Abd al-Karim bin Abi al-Mukhariq, from Musa bin Abi Kathir, from Ibn Abbas (may Allah be pleased with him): that it reached him that Umm Hani (may Allah be pleased with her) mentioned that the Messenger of Allah (peace and blessings be upon him) prayed eight rak'ahs of duha on the day of the Conquest of Makkah.
Important point: Upon this Ibn Abbas (may Allah be pleased with him) said: I had thought that there was a particular prayer for this time, for Allah the Exalted says: "They glorify (Allah) in the evening and at sunrise (ishraq)."

Reference / Source: Ishaq bin Rahawayh narrated it in his "Musnad" (2116) via Yazid bin Abi Ziyad, from Abdullah bin al-Harith, who said: I asked about the duha prayer during the rule of 'Uthman (may Allah be pleased with him), while the Companions were present in large numbers, but no one informed me about it except Umm Hani (may Allah be pleased with her): that the Messenger of Allah (peace and blessings be upon him) came to her house and prayed eight rak'ahs.
Important point: Ibn Abbas (may Allah be pleased with him) said: Whenever I came to this verse ﴿يُسَبِّحْنَ بِالْعَشِيِّ وَالْإِشْرَاقِ﴾ [they glorify (Allah) in the evening and at sunrise], I used to wonder what this "ishraq" was. So (now it is known that) this is the ishraq prayer.
Grading: Yazid bin Abi Ziyad is "hasan" in corroborating chains and supporting reports, especially since Abdullah bin al-Harith is his mawla.
Corroborating chains and supporting reports: This narration is also in Musnad Ahmad 44/ (26901) and 45/ (27391) and in Ibn Majah (1379) via the same route, but the story of Ibn Abbas (may Allah be pleased with him) is not mentioned there.

Reference / Source: Al-Tabarani narrated it in "al-Kabir" 24/ (986) and "al-Awsat" (4246) via Hajjaj bin Nusayr, from Abu Bakr al-Hudhali (Salma), from 'Ata', from Ibn Abbas (may Allah be pleased with him), who said: I used to pass by this verse ﴿بِالْعَشِيِّ وَالْإِشْرَاقِ﴾ [in the evening and at sunrise] and did not know what it was, until Umm Hani (may Allah be pleased with her) told me that the Messenger of Allah (peace and blessings be upon him) came to her house, called for water, performed wudu and prayed the duha prayer, and said: "O Umm Hani! This is the ishraq prayer."
Technical note / Defect ('illah): In this narration the use of the verse as evidence has been attributed directly to the Prophet (peace and blessings be upon him) (marfu'). According to al-Tabarani, no one narrated it from 'Ata' except Abu Bakr al-Hudhali, and Hajjaj bin Nusayr is alone in narrating it.
Grading: Its chain is "very weak" (da'if jiddan): Hajjaj is weak, and his shaykh Abu Bakr al-Hudhali is "matruk" (abandoned).

Reference / Source: Ahmad bin Mani' narrated it in his "Musnad" (as cited in "al-Matalib al-'Aliyah" 3694), and Ibn Shahin in "al-Targhib" (130), via Abu Ahmad al-Zubayri, from Hanzalah bin 'Abd al-Hamid, from al-Dahhak bin Qays, from Ibn Abbas (may Allah be pleased with him), who said: A time passed over us when we did not know what the meaning of this verse ﴿يُسَبِّحْنَ بِالْعَشِيِّ وَالْإِشْرَاقِ﴾ [they glorify (Allah) in the evening and at sunrise] was, until we saw people praying the duha prayer.
Technical note / Defect ('illah): Hanzalah bin 'Abd al-Hamid (who is also called Hanzalah bin 'Abd al-Rahman al-Qass) was declared weak by Ibn Ma'in, and al-Dahhak is a "majhul al-hal" (of unknown condition) narrator.

Important point: Contrary to this earlier report of Ibn Abbas (may Allah be pleased with him) (about not knowing), 'Abd al-Razzaq (4871) narrated via Ibn Jurayj that Sulayman al-Ahwal heard 'Ata' al-Khurasani say to Tawus: Ibn Abbas (may Allah be pleased with him) used to say that the duha prayer is mentioned in the Qur'an, but only a diver reaches its depth; then he recited the verse ﴿يُسَبِّحْنَ بِالْعَشِيِّ وَالْإِشْرَاقِ﴾ [they glorify (Allah) in the evening and at sunrise].
Note / Clarification: Imam Tawus said: By Allah! Ibn Abbas (may Allah be pleased with him) never prayed it until his death, except when he was performing tawaf of the House of Allah.
Grading: Its chain is "sahih".

Grading: This report of Umm Hani (may Allah be pleased with her), that the Prophet (peace and blessings be upon him) prayed eight rak'ahs in her house, is "sahih".
Reference / Source: Imam Ahmad 44/ (26899), Muslim (719) (81), al-Nasa'i (487) and (488) and Ibn Hibban (1187) and (2538) narrated it via two routes from Ibn Shihab al-Zuhri, who transmits from Abdullah bin Abdullah bin al-Harith, from his father Abdullah bin al-Harith, from Umm Hani (may Allah be pleased with her).

Grading: Imam al-Tirmidhi declared this narration "hasan sahih".

Technical note / Defect ('illah): Imam Ahmad (26889) narrated it via Ma'mar, from al-Zuhri, from Abdullah bin al-Harith, in which the intermediary (Abdullah bin Abdullah) between al-Zuhri and Abdullah bin al-Harith has "dropped".

Technical note / Defect ('illah): Ibn Majah (614) and al-Nasa'i (486) narrated it via al-Layth bin Sa'd, from al-Zuhri, from Abdullah bin Abdullah bin al-Harith, in which the name of (the grandfather) Abdullah bin al-Harith has "dropped".

Reference / Source: The other routes of this narration from Umm Hani (may Allah be pleased with her) have already passed under narrations nos. (7043) and (7044).