Is it possible that the person who appeared in a dream, in a TV series, playing the role of the Prophet, peace and blessings be upon him, is actually the Prophet, peace and blessings be upon him?

Seeing the Prophet, peace and blessings be upon him, in a dream is a true vision, and Satan cannot impersonate him. However, a condition for seeing him is that the beholder must see him in his true form as he was. If the beholder describes a characteristic that is unknown, then he has not seen him.

If you wish to know whether the person you saw in the dream is the Messenger of Allah, peace and blessings be upon him, or not, then compare the description of the seen person with what has been narrated in the Sunnah concerning the Prophet's description, peace and blessings be upon him.