What are the descriptions of the Prophet (peace and blessings be upon him) established in the Sunnah, such that if a person sees them in a dream, it is as if they have seen him (peace and blessings be upon him)? And is it permissible to ask him for supplication for someone who sees him in a dream?

If a Muslim sees the Prophet, peace and blessings be upon him, in a dream, depicted with his established characteristics, then he has indeed experienced a true vision, for Satan cannot take his form. However, asking the Prophet, peace and blessings be upon him, for supplication in a dream does not carry any legal ruling, as it does not originate from a deliberate will.