Is it permissible for a Muslim to ask Allaah The Almighty to let him see the Prophet, sallallaahu ‘alayhi wa sallam, in a vision?
Will seeing the Prophet, sallallaahu ‘alayhi wa sallam, in Paradise be something specific to men?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.

Seeing the Prophet, sallallaahu ‘alayhi wa sallam, in a dream is a glad tiding for the believer, because whoever sees him in a dream will see him on the Day of Judgment. The Prophet, sallallaahu ‘alayhi wa sallam, said that whoever sees him in a vision will see him while being awake in the Hereafter, for Satan cannot impersonate him.  Therefore, whoever sees him in a vision will truly have seen him. [Al-Bukhari ] Therefore, there is no harm in a Muslim asking Allaah The Almighty to let him see the Prophet, sallallaahu ‘alayhi wa sallam, in a vision.

With regards to seeing the Prophet, sallallaahu ‘alayhi wa sallam, in Paradise - this is not just for men. Rather, it is for all who obey him, whether male or female, as Allaah The Almighty Says (what means): {And whoever obeys Allaah and the Messenger - those will be with the ones upon whom Allaah has bestowed favor of the prophets, the steadfast affirmers of truth, the martyrs and the righteous. And excellent are those as companions.} [Quran 4:69]

The occasion when the previous verse was revealed was when a man came to the Prophet, sallallaahu ‘alayhi wa sallam, and told him that he loved him very much. However, he was grieved whenever he remembered that he would not be raised to the rank of the Prophet, sallallaahu ‘alayhi wa sallam, in Paradise and consequently would not see him. The Prophet, sallallaahu ‘alayhi wa sallam, did not respond until this verse was revealed. [At-Tabaraani and Al-Maqdisi]

It was also narrated on the authority of a group of the Companions that the Prophet, sallallaahu ‘alayhi wa sallam, said that everyone will be with whom they love. [This Hadeeth has been in most books of Hadeeth.]

Anas said that the Muslims never rejoiced at anything like they did at this statement, as every believer loves the Prophet, sallallaahu ‘alayhi wa sallam.

In addition, it was narrated that the Prophet, sallallaahu ‘alayhi wa sallam, supplicated for Nusaybah Al-Ansaariyyah and her son both, to accompany him in Paradise, as they had asked him to do so. [Ibn Sa‘d]

Allaah Knows best.