Did the Prophet wash his hand before eating?
Did he use soap or something similar, or plain water?
Answers based of sahih hadth would be appreciated.
This hadith can be found in Sunan Abu Dawud, under the chapter "Washing the hands before eating (12)":
Narrated Salman al-Farsi: I read in the Torah that the blessing of food consists in ablution before it. So I mentioned it to the Prophet (ﷺ). He said: The blessing of food consists in ablution before it and ablution after it. Sufyan disapproved of performing ablution before taking food.
Abu Dawud and Albani said this hadith is weak.
This hadith can be found in Sunan Ibn Majah, under the Chapters on Food:
Kathir bin Sulaim narrated that he heard Anas bin Malik say: "The Messenger of Allah (ﷺ) said: ‘Whoever would like Allah to increase the goodness of his house, should perform ablution (wash hands) when his breakfast is brought to him and when it is taken away.’"
Also classified as a weak hadith, according to Darussalam
Although these hadiths are weak, it is OK to follow them since they are considered Fada'el al A'amal (فضائل الأعمال).
Also, as there was no mention of soap, you are free to use whichever material helps clean your hands.