Does seeing the Prophet, peace and blessings be upon him, in a dream smiling and saying, "Ask me for any supplication, and I will supplicate it for you"—then the dream cuts off before the supplication—have a specific meaning, and can disbelievers and profligates see the Prophet in a dream?

This is a good dream, and it is a sign of good for the believer, due to the Prophet's (peace be upon him) saying in interpretation of the verse: "{For them are good tidings in the worldly life}": "It is the righteous dream that the believer sees, or is seen for him." Therefore, whoever sees it should praise Allah and hold fast to his religion even more. As for the interpretation of dreams, it is not within the purview of this website. And as for seeing the Prophet (peace be upon him), both the righteous and the wicked can see him.