Do the souls of believers visit one another in Barzakh, and does the principle of those in higher ranks descending to visit those beneath them apply to seeing the Messenger of Allah, peace and blessings be upon him, in the Exalted Companion?

The souls have dispositions after death, the true nature of which is known only to Allah. There is no evidence to suggest that the inhabitants of higher ranks descend to visit the inhabitants of lower ranks in Paradise. Rather, the people of Paradise do not perceive differences among themselves, and envy and hatred have been removed from their hearts; their hearts are as one.

The inhabitants of lower ranks will see those who are above them without that affecting their souls. As for seeing the Messenger, Allah's peace and blessings be upon him, in Paradise, this is achieved by obeying Allah and His Messenger. Muslims will be with the prophets, the truthful, the martyrs, and the righteous in one abode and one bliss, enjoying seeing them, not by equality in rank. Everyone in Paradise is content with their state.