Are those men( sleepers of cave) still alive? They are in deep sleep like they were or they are dead?

Because I have heard that those people will come back when the Imam comes. In Amman Jordan the grave are real?

Will Imam awaken those people or make them alive?

Refer me an authentic book were I can read the full details history according to ahlulbait hadiths

No they are not alive. They passed away and were buried in the cave.

Yes, we have narrations that when Imam Mahdi (a) appears, they will be resurrected by Allah and they will support the Imam.

Scholars have different opinions about where the cave is. Many believe it is in Jordan.

Some further readings on them:

https://www.al-islam.org/hayat-al-qulub-vol-1-allamah-muhammad-baqir-al-majlisi/account-people-cave-and-inscription

https://www.al-islam.org/enlightening-commentary-light-holy-quran-vol-9/section-2-companions-cave