Is it possible for someone who worships God and adheres to religious obligations, yet commits minor sins such as listening to music and teaching women, to see the Prophet in a dream? And is this vision real?

The Prophet’s (peace and blessings be upon him) vision is true, because Satan cannot impersonate him. It is not exclusively for the obedient, and it may contain a warning and glad tidings for the questioner to cease his transgressions and adhere to the Sunnah of the Prophet (peace and blessings be upon him), while noting that persistence in minor sins transforms them into major ones.