Praise be to Allah.

Yes, it is proven that the souls of the believers meet and visit one another. There follow some of the ahaadeeth which indicate that, as well as some of the fatwas of the scholars on this matter. 

It was narrated from Abu Hurayrah that the Prophet (peace and blessings of Allaah be upon him) said: “When the believer is dying, the angels of mercy come to him with white silk and say: ‘Come out content and with the pleasure of Allaah upon you to the mercy of Allaah, fragrance and a Lord Who is not angry.’ So it comes out like the best fragrance of musk. They pass him from one to another until they bring him to the gate of heaven, where they say: ‘How good is this fragrance that has come to you from the earth!’ Then the souls of the believers come to him and they rejoice more over him than any one of you rejoices when his absent loved one comes to him. They ask him: ‘What happened to So and so, what happened to So and so?’ They say: ‘Let him be, for he was in the hardship of the world. When he says, ‘Did he not come here?’ They say: ‘He was taken to the pit (of Hell).’ When the kaafir is dying, the angers of punishment come to him with sackcloth and say: ‘Come out discontent and subject to divine wrath to the punishment of Allaah. So it comes out like the foulest stench of a corpse. They bring him to the gates of the earth, where they say: ‘How foul is this stench!’ Then they bring him to the souls of the kuffaar.” Narrated by al-Nasaa’i, 1833; classed as saheeh by al-Albaani in al-Silsilah al-Saheehah, 2758. 

Shaykh al-Islam Ibn Taymiyah said: Does his soul meet with the souls of his family and relatives? According to the hadeeth narrated from Abu Ayyoob al-Ansaari and others of the salaf, and narrated by Abu Haatim in al-Saheeh from the Prophet (peace and blessings of Allaah be upon him):  “When his soul is taken up it is met by the souls who ask him about the living and they say to one another: ‘Let him rest.’ And they say: ‘What happened to So and so?’ And he says: ‘He did a righteous deed.’ They say: ‘What happened to So and so?’ and he says: ‘Has he not come to you?’ They say: ‘No.’ They say: ‘He was taken to the Pit (of Hell).’” 

And because the deeds of the living are shown to the dead, Abu’l-Darda’ used to say: “O Allaah, I seek refuge with You from doing any deed that would shame me before ‘Abd-Allaah ibn Rawaahah.” This is how they meet when he comes and they ask him questions and they answer him. 

With regard to where they settle, that depends on their status before Allaah. For the one who is among those who are close to Allaah (al-muqarrabeen – cf. al-Waaqi’ah 56:88), his status will be higher than those of the Right Hand (cf. al-Waaqi’ah 56:90). The one who is higher may descend to the one who is lower but the one who is lower cannot ascend to the one who is higher, thus they will gather when Allaah wills as they used to gather in this world, despite their differences in status, and they will visit one another. 

That will happen whether their places in which they are buried in this world are far apart or close together. Souls may meet even though their places of burial are far apart, or they may be separated even though their places of burial are close together. A believer may be buried beside a kaafir, but the soul of the former will be in Paradise whilst the soul of the latter is in Hell. Two men may be sitting or sleeping in the same place, but the heart of one is blessed and the heart of the other is tormented, and there is no connection between the two souls. As the Prophet (peace and blessings of Allaah be upon him) said, “Souls are troops collected together and those who got along with each other (in the heaven from whence they come) would have an affinity with one another (in this world) and those amongst them who opposed each other (in heaven) would also be divergent (in the world).” Narrated by Muslim, 2638; Majmoo’ al-Fataawa, 24/368. 

Ibn al-Qayyim said: 

The second issue is whether the souls of the dead meet one another, visit one another and talk to one another. 

This is a good question. The answer is that souls are of two types: those that are punished and those that are blessed.  Those that are punished are too preoccupied with the torment that they are facing to visit and meet one another, but the souls that are blessed are free and are not detained, so they meet one another, visit one another and talk about what they used to do in this world and what happened to the people of this world. So each soul will be with its friends who did similar good deeds. The soul of our Prophet Muhammad (peace and blessings of Allaah be upon him) is with the highest companions. Allaah says (interpretation of the meaning): 

“And whoever obeys Allah and the Messenger - those will be with the ones upon whom Allah has bestowed favor of the prophets, the steadfast affirmers of truth, the martyrs and the righteous. And excellent are those as companions.”

[al-Nisa’ 4:69]

This togetherness is confirmed in this world, in al-Barzakh and in the abode of reward (Paradise), and “A man will be with those whom he loves” in these three realms… Allaah says (interpretation of the meaning): 

“(It will be said to the pious — believers of Islamic Monotheism): ‘O (you) the one in (complete) rest and satisfaction!

28. ‘Come back to your Lord,—  well‑pleased (yourself) and well‑pleasing (unto Him)!

29. ‘Enter you then among My (honoured) slaves,

30. ‘And enter you My Paradise!’”

[al-Fajr 89:27-30] 

i.e., enter among them and be one of them. This is said to the soul at the time of death… And Allaah has told us that the martyrs are: “are alive, with their Lord, and they have provision” [Aal ‘Imraan 3:169]; they “rejoice for the sake of those who have not yet joined them, but are left behind” [Aal ‘Imraan 3:170] and “They rejoice in a grace and a bounty from Allaah” [Aal ‘Imraan 3:171]. This indicates that they will meet one another in three ways: (1) they are with their Lord and are given provision, and if they are alive then they meet one another; (2) they rejoice at the arrival of their brothers and their meeting with them; and (3) the word yastabshiroon (translated as “rejoice”) implies that they pass the good news to one another.  Al-Rooh, p. 17, 18. 

There are ahaadeeth which state that the dead visit one another and we are commanded to make their shrouds beautiful because of that, but none of these ahaadeeth are saheeh. For example, the hadeeth of Abu Qataadah according to which the Prophet (peace and blessings of Allaah be upon him) said: “Whoever takes the responsibility of preparing his brother for burial, let him make his shroud beautiful, for they visit one another in them.” Shu’ab al-Eemaan, 7/10. 

Its isnaad includes Salam ibn Ibraaheem al-Warraaq whom Ibn Mu’een and al-Dhahabi classed as a liar, as did others. 

And Allaah knows best.