Is seeing the Prophet (peace be upon him) in a dream without remembering its details considered a true vision, and is there an interpretation for what was seen in the dream about one of his wives committing adultery after his passing (peace be upon him) and then repenting?

If the description of the Messenger of Allah, peace and blessings be upon him, which is firmly established in the authentic Sunnah, matches what you saw in your dream, then you have indeed seen him, for Satan cannot impersonate him. However, legal rulings are not built upon dreams, and adultery in a dream may be interpreted as something other than actual adultery. We apologize for not interpreting the dream, as the website is not specialized in that.