Barzakh (Arabic: برزخ, from Persian barzakh, "barrier, partition" is an Arabic word meaning "obstacle", "hindrance", "separation", or "barrier") designates a place between hell and heaven, where the soul resides after death, and experiences its own heaven or hell, until the resurrection on Qiyamah (Judgement Day).
Barzakh is the world after this world which starts from death and goes on till the day of Judgment. It is mentioned in Quran (There is a Barzakh after their death till the day of they will be resurrected) (Sura 23, Verse 100).
Barzakh includes the grave but it is wider than the grave. Grave starts on burial but Barzakh starts on death which is before burial.
The pious believer's grave is a garden from the Paradise while the grave of the disbeliever is a ditch from the hellfire, as the Hadeeth states.
Those believers who repent doing wrong, and sincerely seek forgiveness, after giving back the right of others, should not be punished neither in the Day of Judgement nor in Barzakh , after they have been forgiven by Allah (SWT).
The Qur'an and hadith (both Sunni and Shi'i) give the sense that the jinn exist in the same world as us. The Qur'an and hadith describe occasional interactions between humans and jinn on a physical level - for instance, seeing a jinn manifest as an animal (as in the story of the jinn who came to see Imam Ali in the Mosque of Kufa) or hearing their voices audibly. Another example would be the jinn working for the prophet Sulayman (A).
However, apart from those occasional interactions, usually jinn keep to themselves and human beings do not see them.
However, some mystics have held that there is a sort of veil between the human world and the jinn world, which you could call the barzakh. That is, humans and jinn subsist in the same realm, but in something akin to parallel dimensions. I am not aware of any basis for this in Qur'an and hadith, but it could be true.
So do jinn live in the barzakh? To me, the best view is "maybe" and "it depends on what you call the barzakh". If one takes "barzakh" to mean something akin to "mundus imaginalis" - that is, the imaginal realm which humans access through dreams, visions, or imagination, it might be correct to say that jinn live in barzakh. After all, people usually encounter jinn in dreams or the inner realm (for instance, Shaytan whispering to the heart), rather than in physical life. This is similar to how people are more likely to have a dream or vision of a deceased person, such as Imam Husayn (A), rather than physically seeing them walking down the street.
If one takes barzakh to mean specifically the place where human spirits go after death but before the Resurrection... while this meaning of "barzakh" may have some relationship to the above, I am not aware of any texts which specifically say that deceased human spirits live in the same place as living/deceased jinn, although I don't think we have any texts that rule out any sort of interaction ever between living/deceased jinn and deceased humans.
In any case, it seems as if the existence of the human being after death is more similar to the jinn, because the human being in the barzakh is less encumbered by the physical body and able to move around more.
In fact, I don't think we have any texts that say what happens to jinn after they die but before the Resurrection - for instance, do they go to their own barzakh? - however, the Qur'an says that, after Resurrection and Judgment, the jinn who go to Hell and the humans who go to Hell are all mixed together in the same Hell. It does not specify whether the jinn who go to Heaven and the humans who go to Heaven go to the same Heaven.
Anyway, it can be quite difficult to make concrete statements about spiritual cosmology, metaphysical realities, or other things which are not tangible. Even if someone says something, it is really quite difficult to prove whether it is true or false, except in the case of Qur'an and accurate hadith, which we accept on the basis of them being divinely inspired or approved.
So, this, in short, is my understanding of what the Qur'an and hadith say, and also what some mystically inclined thinkers have said. God knows best!
Jinn have their own world and we are not supposed to deal with them nor are we responsible about anything in their world. Those humans who seek help from Jinn will suffer more.
The grave of the sincere obedient believer is a garden from Paradise as the Hadeeth says. In Sura Al-Waqi'ah we read how the great pleasant result of sincere faith and obedience starts immediately on the time of death. The happiness of the sincere believers starts on leaving this world and their Barzakh is the beginning of the happiness of Paradise.
The prophets and their successors are infallible and they are the most humble servants of Allah (SWT). Their life is not limited to this world but continues as we read in Quran ( and don't think that those who were martyred in the way of Allah are dead, nay, they are alive with their Lord getting sustenance. (Sura 3, Verse 169). Prophets and their successors are higher in degree than the martyrs, so, they are alive with Allah.
Every Muslim salutes the Prophet in every Salaah ( ASSALAMU ALAYKA AYYUHAN NABIYYU WA RAHMATULLAH WA BARAKATUH) which means that the Prophet is alive.
We have many authentic Hadeeths that the Prophets are alive in their graves. ( الانبياء أحياء في قبورهم يصلون)
Seeking help from them after their demise is just like seeking help from them before their demise, as Allah (SWT) grants them the ability to help sincere believers by His permission.
The Barzakh of the prophets and Infallible Imams and their sincere followers is part of Paradise, while the Barzakh of their enemies is part of hellfire. The Hadeeth states: The grave of the believer is a garden from the gardens of the Paradise, and the grave of the non believer is a dig from the digs of Hellfire.
Peoples' rank may be elevated in Barzakh, however, not due to any voluntary act they perform there since the book for their actions is closed. It may be elevated because of some good work that they have left behind and the effects of it reaches them after their death, or due to charities or acts done on their behalf by their friends or relatives. There may also be other causes like breezes of mercy coming from the Lord every now and then.