How many cases of stoning are documented in the hadith? Were all of them carried out on the Jews or were Muslims also stoned for adultery?
There are at least four cases of Muslims being stoned to death according to the Hadd of Zina (adultery) in the time of the Prophet, as recorded in the major Hadith collections.
Maiz ibn Malik of the tribe of Aslam:
A man from the tribe of Aslam came to the Prophet (ﷺ) and confessed that he had committed an illegal sexual intercourse. The Prophet (ﷺ) turned his face away from him till the man bore witness against himself four times. The Prophet (ﷺ) said to him, "Are you mad?" He said "No." He said, "Are you married?" He said, "Yes." Then the Prophet (ﷺ) ordered that he be stoned to death, and he was stoned to death at the Musalla. When the stones troubled him, he fled, but he was caught and was stoned till he died. The Prophet (ﷺ) spoke well of him and offered his funeral prayer. [Saheeh Bukhari]
When Ma'iz bin Malik came to the Prophet (in order to confess), the Prophet (ﷺ) said to him, "Probably you have only kissed (the lady), or winked, or looked at her?" He said, "No, O Allah's Messenger (ﷺ)!" The Prophet said, using no euphemism, "Did you have sexual intercourse with her?" The narrator added: At that, (i.e. after his confession) the Prophet (ﷺ) ordered that he be stoned (to death). [Saheeh Bukhari]
The Messenger of Allah (ﷺ) asked Ma’iz b. Malik : Is what I have heard about you is true? He said: What have you heard about me? He said: I have heard that you have had intercourse with a girl belonging to the family of so and so. He said: Yes. He then testified four times. He (The prophet) then gave order regarding him and he was stoned to death. [Sunan Abu Daud]
Then a woman of Ghamid, a branch of Azd, came to him and said: Messenger of of Allah, purify me, whereupon he said: Woe be upon you; go back and beg forgiveness from Allah and turn to Him in repentance. She said: I find that you intend to send me back as you sent back Ma'iz. b. Malik. He (the Holy, Prophet) said: What has happened to you? She said that she had become pregnant as a result of fornication. He (the Holy Prophet) said: Is it you (who has done that)? She said: Yes. He (the Holy Prophet) said to her: (You will not be punished) until you deliver what is there in your womb. One of the Ansar became responsible for her until she was delivered (of the child). He (that Ansari) came to Allah's Apostle (ﷺ) and said the woman of Ghamid has given birth to a child. He (the Holy Prophet) said: In that case we shall not stone her and so leave her infant with none to suckle him. One of the Ansar got up and said: Allah's Apostle, let the responsibility of his suckling be upon me. She was then stoned to death. [Saheeh Muslim]
"A woman from Juhainah confessed before the Prophet (ﷺ) that she had committed adultery, and she said: 'I am pregnant.' So the Prophet (ﷺ) called for her guardian and said: 'Be good to her and if she gives birth to her child then tell me.' So he did so, and then he (ﷺ) gave the order that her clothes be bound tightly around her. Then he ordered her to be stoned and she was stoned. Then he performed (funeral) Salat for her. So 'Umar bin Al-Khattab said to him: 'O Messenger of Allah! You stoned her then you prayed for her?!' He said: 'She has repented a repentance that, if distributed among seventy of the people of Al-Madinah, it would have sufficed them. Have you ever seen something more virtuous than her sacrificing herself for the sake of Allah?'" [ Saheeh Muslim ]
Unnamed woman who committed adultery with an unmarried man:
A bedouin came to the Prophet (ﷺ) while he (the Prophet) was sitting, and said, "O Allah's Messenger (ﷺ)! Give your verdict according to Allah's Laws (in our case)." Then his opponent got up and said, "He has told the truth, O Allah's Messenger (ﷺ)! Decide his case according to Allah's Laws. My son was a laborer working for this person, and he committed illegal sexual intercourse with his wife, and the people told me that my son should be stoned to death, but I offered one-hundred sheep and a slave girl as a ransom for him. Then I asked the religious learned people, and they told me that my son should be flogged with one-hundred stripes and be exiled for one year." The Prophet (ﷺ) said, "By Him in Whose Hand my soul is, I will judge you according to Allah's Laws. The sheep and the slave girl will be returned to you and your son will be flogged one-hundred stripes and be exiled for one year. And you, O Unais! Go to the wife of this man (and if she confesses), stone her to death." So Unais went in the morning and stoned her to death (after she had confessed). [Saheeh Bukhari]
Unnamed man who committed rape:
A women went out during the time of the Prophet (ﷺ) to go to Salat, but she was caught by a man and he had relations with her, so she screamed and he left. Then a man came across her and she said: 'That man has done this and that to me', then she came across a group of Emigrants (Muhajirin) and she said: 'That man did this and that to me.' They went to get the man she thought had relations with her, and they brought him to her. She said: 'Yes, that's him.' So they brought him to the Messenger of Allah (ﷺ), and when he ordered that he be stoned, the man who had relations with her, said: 'O Messenger of Allah, I am the one who had relations with her.' So he said to her: 'Go, for Allah has forgiven you.' Then he said some nice words to the man (who was brought). And he said to the man who had relations with her: 'Stone him.' Then he said: 'He has repented a repentance that, if the inhabitants of Al-Madinah had repented with, it would have been accepted from them.'" [Sunan Abu Daud and Jami Tirmizi]
Finally, the Jewish couple who committed adultery and were stoned according to the law of the Torah:
A Jew and a Jewess were brought to Allah's Messenger (ﷺ) on a charge of committing an illegal sexual intercourse. The Prophet (ﷺ) asked them. "What is the legal punishment (for this sin) in your Book (Torah)?" They replied, "Our priests have innovated the punishment of blackening the faces with charcoal and Tajbiya." Abdullah bin Salam said, "O Allah's Messenger (ﷺ), tell them to bring the Torah." The Torah was brought, and then one of the Jews put his hand over the Divine Verse of the Rajam (stoning to death) and started reading what preceded and what followed it. On that, Ibn Salam said to the Jew, "Lift up your hand." Behold! The Divine Verse of the Rajam was under his hand. So Allah's Apostle ordered that the two (sinners) be stoned to death, and so they were stoned. Ibn `Umar added: So both of them were stoned at the Balat and I saw the man sheltering the woman. [Saheeh Bukhari]